The zero-crossing isn't marked in Live, so it might be a bit difficult to explain, but most audio programs show the zero-crossing. The zero-crossing is a horizontal line across a waveform that shows where zero db is on the waveform. This also represents where the speaker is at it's rest position as it vibrates back and forth. The farther the signal is from zero the further the speaker is from it's rest position. This also corresponds to how intense, or "loud", the signal is...although "loudness" is a much more complex issue than just how far the speaker is from center...
The reason its important to cut audio at the zero crossing is that if you don't, the signal has to jump from wherever it was, to zero, or some other value, instantly, which is not possible. So you hear a "pop" when that happens. This also accounts for glitching in audio, from digital clipping or bad rendering or whatever. When a digital signal clips, the signal information has gone outside the boundaries of what can be recorded, so a maximum or minimum signal value is recorded instead...meaning that wherever the signal was, it jumps to this new value, causing a "pop" or crazy distortion sound if the corruption goes on for very long.
This also ties in to "DC Offset" which is when the zero-line of an audio file doesn't correspond to the actual zero-line for digital audio. This can happen through the course of processing a sound or a number of other ways. If the DC Offset is not corrected, the sound can be fatiguing and even damage speakers, because the speakers and eardrums are not returning to their rest position but to some offset position. Fortunately most audio programs (SoundForge, Cubase, ProTools, etc..) can quickly and easily correct DC Offset across an entire audio file. There are also VST's that can accomplish this on the fly.
Well, that's my understanding of this issue at least. Hope it's of some help
