Fly727 has the best description.
But remember the principle behind the TCAS system is that the a/c equipped with a TCAS interrogates the other a/c in the sky (like an ATC radar would), and analyses the reply. Now the altitude of the other a/c will be given by its encoding altimeter (ADC on bigger airplanes).
Given that, a TCAS equipped a/c won't "see" the other plane if that plane's transponder is turned off, or if the mode c (altitude reporting) is not working correctly. If the encoding is wrong, then the TCAS won't "see" the correct altitude.
A/C equipped with TCAS II
systems have at least one mode-S xpder with the 24-bit binary code specific to the a/c. (For example, if 2 planes with TCAS II
systems come face to face, since the code is different, one will get instructions to go up, the other to go down) The pilot will know how much he needs to climb or descend because a green stripe will appear on his VSI (Resolution Advisory (RA)) to show him where to go, the remainder will usually be in red (meaning don't go this way or you could collide).
The deadline for TCAS II
installation for many airplanes here in North America is early 2005 (turbine powered and more than 12 500 pounds I believe). There are many older business jets to be upgraded, which usually have a TCAS I, that is when they have a TCAS installed at all.
People sometimes confuse TCAS (Traffic Collision Avoidance System) with the GPWS (Ground Proximity Warning System). The latter will for example tell you to "WHOOP WHOOP PULL UP
!!!" when you're about to crash in the ground.
Then you have the EGPWS and TAWS, but like mentioned above, that's more Tech/Ops stuff.
Hope this helps,