DAC (and ADC) are huge topics and would need a complete engineering course. But let us see if we can understand it in a simple way.
After the definition, I am going to add some fun by delving on two controversial topics. One is the need for an external DAC, and the second is whether the analogue form is better than the digital form.
BEGIN DEFINITION
Analog describes any fluctuating, evolving, or continually changing process. A base carrier's alternating current frequency is modified in some way, such as by amplifying the strength of the signal or varying the frequency, in order to add information to the signal. This information is then stored or broadcast.
Digital describes electronic technology that generates, stores, and processes data in terms of two states: positive and non-positive. Positive is expressed or represented by the number 1 and non-positive by the number 0. Thus, data transmitted or stored with digital technology is expressed as a string of 0's and 1's. Each of these state digits is referred to as a bit. A group of 8 bits is referred to as a byte. .
An audio signal is converted to electrical signals for storage and distribution. Because sound has notes (pitch) and volume (loudness or amplitude), it is represented by a sine wave. The pitch of a musical note is the same as its frequency. The intensity or loudness of a musical note is the same as its amplitude. The third element is the time domain that is represented in the sine wave by a cycle. The term, sine wave, originated because the modulation of the carrier wave is analogous to the fluctuations of the human voice or other sound that is being transmitted.
When you take something as simple as alphabets and numbers, they have fixed representation in digital form, mostly consisting of eight bits for alphabets and four bits for numbers. Thus the representation of alphabets and numbers is digital form is very simple. For example an 'a' is always 01100001 in its binary form.
A sound wave, represented by a sine wave, is a different thing altogether. A sine wave is continuous and has infinite number of datum, that keeps changing continuously. To represent this in digital form, you need to do what is called sampling. In sampling, you represent the sine wave over periodic intervals in a digital wave form, and then convert it back to a sine wave by interpolating the data. Sampling is usually carried out in two stages, discretization and quantization. In the discretization stage, the space of signals is partitioned into equivalence classes and quantization is carried out by replacing the signal with representative signal of the corresponding equivalence class. In the quantization stage the representative signal values are approximated by values from a finite set.
In order for a sampled analog signal to be reconstructed, the Nyquist-Shannon sampling theorem must be satisfied. This theorem states that the sampling frequency must be greater than twice the bandwidth of the signal. In practice, the sampling frequency is often significantly more than twice the required bandwidth. The most common bandwidth scenarios are: DC - BWx (baseband); and Fc +/-BWx, a frequency band centered on a carrier frequency ("direct demodulation").
An analogue to digital converter (ADC) converts analogue signals to digital signals. A digital to analog converter (DAC) is used to convert the digital signal back to analog. In general the operations of a ADC and a DAC come under the domain of Digital Signal Processing.
END DEFINITION
Now to the fun part.
Processing of pure digital form is quite simple as it consists of a finite number of elements. That is the reason why, when you save a text file in a computer, you always get the same text any number of times. The data never changes, unless you change it. Of course you can lose the data if the hard disk fails, but that is a electro-mechanical issue, and has nothing to do with the digital form of storing data. Even this has become very rare, if you follow some simple procedures. In my 25 years of working with computers, I have never, never lost one byte of data. One important point here - when reading or writing data, the head of a disk drive never touches the drive platter.
Now take a tape drive. The tape has a magnetic coating in which the data is written in the form of frequency variation. Remember magnetism is never permanent unless it has some energy driving it. All magnets lose their intensity over time.
To write and read, the head must touch the tape. In the process there is a continuous decay of the coating. Remember the need to clean the brown stain off read/write head with Isopropyl Alcohol? That is a bit of magnetic coating removed from the tape. Similarly, when you consider a turntable, the cartridge has a small needle that is scratching the disc. Again every time you play the disc, you are enlarging and deepening the pit, thereby modifying the data. .
In other words, every time you use a tape drive of a turntable, you are slowing destroying the data, or adding data in the form of noise. This can never happen in a digital format, as there is no mechanical friction of any kind.
Now to my FIRST fun point. External DACs such a the famous DAC1 from Benchmark uses AD1853, a Stereo, 24 Bit, 192 kHz, Multibit Sigma-Delta DAC. Good CD players such as those from NAD, Cambrudge Audio, Rotel etc use chips such as Burr Brown's PCM1737 which is a 24-Bit 192-kHz Sampling Advanced-Segment Audio Stereo DAC. If you look at the specs of these chips, they are very very close to each other, if not identical. Since both DAC circuitry (assuming they are both designed and built well) work on the same finite number of digital data, and send them to the same pre/power amplifier, how much difference can an external DAC make to an already excellent DAC that is inside the CD Player? If at all it does make a difference, it should be of very small magnitude, say less than 5%, to the quality of the sound.
If you read Stereophile, John Marks enthusiastically wrote about the Benchmark Media Systems DAC1 D/A processor and headphone amplifier. Comparing its sound playing CDs with that of a three-times-more-expensive Marantz SA-14 SACD player, he concluded that the DAC 1's "Red Book" performance was at least as good as that of the Marantz, being "slightly more articulate in the musical line, and slightly more detailed in spatial nuances, particularly the localization of individual images in space, and in soundstage depth."
In my mind, these are subjective terms that anybody can use positively or negatively as is required. Everything is slightly more?
Now to my SECOND fun point. An original analogue sound properly converted through a ADC to digital, cut well into a CD (or let us say as uncompressed data in an hard disk), would always provide consistent information for playback and amplification. Irrespective of how many times you use the data, the information will be the same. Assuming you use a good CD player, a good DAC, and the same pre/power amplifier after the source, the sound from the digital source should consistently be better than from an analogue source such as a Turntable.
I show below Lie Number 3 - The AntiDigital Lie - from the Ten Biggest Lies in Audio. This is written by Peter Aczel in his 26th Issue of The Audio Critic. I just quote the exact text below. I am sorry if his wordings are a little harsh.
QUOTE
2. THE ANTIDIGITAL LIE
You have heard this one often, in one form or another. To wit: Digital sound is vastly inferior to analog. Digitized audio is a like a crude newspaper photograph made up of dots. The Nyquist-Shannon sampling theorem is all wet. The 44.1 kHz sampling rate of the compact disc cannot resolve the highest audio frequencies where there are only two or three sampling points. Digital sound, even in the best cases, is hard and edgy. And so on and so forth. All of it, without exception, ignorant drivel or deliberate misrepresentation. Once again, the lie has little bearing on the mainstream, where the digital technology has gained complete acceptance; but in the byways and tributaries of the audio world, in unregenerate high-end audio salons and the listening rooms of various tweako mandarins, it remains the party line.
The most ludicrous manifestation of the antidigital fallacy is the preference for the obsolete LP over the CD. Not the analog master tape over the digital master tape, which remains a semi-respectable controversy, but the clicks, crackles and pops of the vinyl over the digital data pits' background silence, which is a perverse rejection of reality. Here are the scientific facts any second-year E.E. student can verify for you: Digital audio is bulletproof in a way analog audio never was and never can be. The 0's and l's are inherently incapable of being distorted in the signal path, unlike an analog waveform. Even a sampling rate of 44.1 kHz, the lowest used in today's high-fidelity applications, more than adequately resolves all audio frequencies. It will not cause any loss of information in the audio range not an iota, not a scintilla. The "how can two sampling points resolve 20 kHz?" argument is an untutored misinterpretation of the Nyquist-Shannon sampling theorem. (Doubters are advised to take an elementary course in digital systems.)
The reason why certain analog recordings sound better than certain digital recordings is that the engineers did a better job with microphone placement, levels, balance, and equalization, or that the recording venue was acoustically superior. Some early digital recordings were indeed hard and edgy, not because they were digital but because the engineers were still thinking analog, compensating for anticipated losses that did not exist. Today's best digital recordings are the best recordings ever made. To be fair, it must be admitted that a state-of the-art analog recording and a state-of-the-art digital recording, at this stage of their respective technologies, will probably be of comparable quality. Even so, the number of Tree-Worshiping Analog Druids is rapidly dwindling in the professional recording world. The digital way is simply the better way.
UNQUOTE