True bypass is when you turn your effect off (bypass it) and your sound isn't affected by the pedal/stompbox/whatever.. Most likely, when you use a digital effects processor, you don't have true bypass, the sound is always a bit altered by the processor.. It's best to buy something with true bypass, so you have the original sound of your guitar and amp..
Hope that helped a little..
Thats basically it ^

An example of a true bypass is BBE. And I have yet to find a BBE that wasnt a great pedal.
yea, true bypass is ok, it really depends on how it gets used, there are non true bypass pedals that suck less tone than true bypass ones do.

as for true bypass itself, its not really important, its mostly 'mojo'

now, that being said, some non true bypass pedals suck alot of tone, but if done right you can end up with a better bypass than true bypass