The L/R inputs correspond to mixer buses. If I have a 4-buss mixer, and I want to record 4 tracks independently from it, I assign the buses/tracks as follows: Bus 1>Track 1 L; Bus 2>Track 2 R; Bus 3>Track 3 L; Bus 4>Track 4 R.
The L/R thing is a legacy term left over from tape deck recording. The fact is that you can take a track you have recorded from L, for example, and pan it where ever you want. In fact, with Cool Edit Pro/Adobe Audition, the playback will default to centered until you change it with the "pan" button or the pan envelope.
The issue about stereo recording is a little more complex. What you want to accomplish with the finished mix is to emulate a soundstage, where each instrument comes from an area from left to right and front to back (as always, there are exceptions, but we'll ignore them). If you record each instrument in stereo, you'll end up with mud, because each stereo image will be trying to establish that "its" image is the right one, and your ears get confused. So, by recording each track in mono, we simplify the problem, and reduce it to something resolvable in the mixdown. That is, we have a single, mono track of guitar, say, and we pan it over there, and then we put a mono keyboard track and we pan it over here. When all is done it sounds as though the guitar is being played "over there", and the keyboard is being played "over here."
There are exceptions to mono recording: foremost is the drum part. I have a small space, so I depend on a drum machine, which I record in stereo, panned fairly closely around the center. This allows me to preserve the image of a drummer ("see, his snare is just to the left, and his toms are just to the right, and the kick is dead center") and I mix the rest of the song around the drum tracks.
Another exception would be a song featuring solo piano: it will sound a lot more natural if you record it in stereo.
But many other instruments and sources sound less cluttered, and exhibit fewer phase problems, if you simply record to mono. Even vocal choruses: I like to record the same track with 2 different mics, then pan them differently and possibly EQ them a little differently so that each voice is more distinct. While this may sound like stereo recording, it's really "dual-mono'; each part is on its separate track and I have the option, if necessary later on in the mixing process, to use only one track. This depends only on how it sounds, and on how I want it to sound.
Hope this helps. This is a very elementary run-through of the issues involved.
