I always had this question in mind. I understand this phenomenon for speakers, CD transports, etc as they are mechanical devices. Burn-in period for speakers can be related to run-in period for cars, for example. I never understood this phenomenon for electronics.
Is it our auditory system that is getting used to new sound signature? What sounded shrill initially appears fine over time. For example, when I moved to Bangalore, I found it hard to drive initially due to relentless honking and I even experienced headaches after spending long time in traffic. Over time, I got used to it.
Another explanation could be the coping mechanism within ourselves. For many like me, a good audio system severely dents the bank balance. For many others who are well settled, it is still a portion of the hard earned money that is spent. We also invest a lot of time and effort while hunting for a system. The more time, money and effort we put in, the higher will be our expectations. Finally the system we pick may fall behind these expectations. We take time to digest this fact, and accept and learn to live with what we have. Our mind can find ways to see us through this process, which psychologists call coping mechanism.
I am an electronics engineer, and I don't have the luxury to deliver a product that doesn't meet my customer's expectations and then make a claim that it will get better over time. Wish I were working in high-end audio field. I am also bound to give rational explanation to various phenomenon. The first one about the behavior of human auditory systems is Biology and the other about coping mechanism is psychology; both, outside my domain. If I accept this phenomenon for audio, then I will be tempted to apply the same to other systems where I am involved in the design, as well. So, whenever someone talks about electronics sounding better over time, I always choose the neutral camp.