One of the challenges when designing a speaker is what to do with the "back wave", ie the signal off the back of the speaker. If you don't do anything, then the back wave cancels out the front wave at lower frequencies -- that's why a speaker sitting out on the table always sounds tinny unless you put it in an enclosure.
There are a variety of different things you can do with the back wave. The simplest is a sealed and damped box ("acoustic suspension") which absorbs the back wave and provides extra "spring" for the woofer cone, but the downside is that the extra spring raises the resonant frequency of the speaker so you can lose some deep bass.
Bass Reflex speakers use a tuned, resonant enclosure with a port so that at a specific frequency the back wave coming out of the port has been inverted and is now in phase with the signal coming off the front of the speaker. This gives you a nice bass boost right at the point where the speaker would otherwise be rolling off, and the resonating air inside the enclosure helps to control cone movement at very low frequencies but doesn't affect the resonant frequency as much as a sealed box.
A transmission line accomplishes pretty much the same thing but actually uses a long folded path so that the time delay from speaker to port is enough to bring the back wave in phase with the front wave.
The idea of Infinite Baffle comes from the use of a baffle board (a board with the speaker mounted in it) which provided better LF response by keeping the front and back waves apart until much lower frequencies -- the bigger the board, the lower frequencies you can get before the front and back wave combines. An Infinite Baffle uses the wall and room behind to provide the same effect as an infinitely large baffle board.
You could also call it an infinitely large sealed enclosure but AFAIK most IB fans think sealed subs are wussy
