A HDMI pass through is any device that has one or more HDMI inputs and one or more HDMI outputs. What ever data comes through the input is 'passed' along without any processing whatsoever to one of the outputs.
A repeater is more complicated. Repeater is a concept borrowed from computer networking technology, and could repeat (with amplification), switch, distribute, duplicate, or protect the signals.
A simple repeater has a small amplifier that can be used to extend an audio or video signal beyond the standard length specified for the cable.
A repeater that acts as a switch will take input from a multiple sources such as two DVD Players and send it one device, such as a TV. Irrespective of which DVD Player you use, you will be able to see the image on the TV.
A repeater that acts as a distributor takes input from a single device such as one DVD Player and sends it to multiple devices such as, say, TVs. As a distributor, only one output device will work at any one time. If more than one device is to be active, the repeater can also act as a duplicator.
With specific relation to TV signals, repeater can also act as a protector of digital rights for HDCP signals. HDCP stands for High-bandwidth Digital Content Protection. HDCP data is usually stored and transmitted with encryption. A repeater will be able to receive this signal, decrypt it, and play it through an amp for you.
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