There are generally three distinct phases of recording: tracking, mixing and mastering.
TRACKING: the process of getting the sounds ON TAPE (or whatever). Probably the most crucial area of recording happens hear because if you record crap, chances are the best mixers and mastering guru's can't help you. Maybe they can polish that turd, but it still won't be great.
Tracking is a delicate art--part science, part artwork, part guesswork (you have to visualize the final composition and how it will sound together). The science is knowing how to set gain levels, getting a clear and clean signal to tape; the creative part is doing non-regulation weird stuff or choosing how you mic something--like should I have one overhead pointing at the snare, or should I have an XY over the drummer's head, or how about adding some 414's on omni to capture the room?
MIXING: once you have everything recorded to its own seperate track the next step is to MIX them together. Mixing is where you take those 1000 things recorded all fighting for the same space in the mix and give them their own space. You also decide how much (LOUD) and the stereo placement of each item. Mixing is built on two things: COMPRESSION and EQ.
Believe it or not compression is the most vital and contributes more than anything else to a professional sound (when used right) than anything else in the mixing stage other than your basic levels. EQ can change the tone/timbre of a track and also to carve out niches so the listener can hear what's going on in the song without it turning into mud.
After compression and EQ comes reverb--probably the third most important effect during the mixing process. By using this you can accentuate your stereo image and give the illusion that certain elements are further away--creating depth to your mix. Reverb also smooths out things like cymbals and vocals. The key to remember about reverb is a little bit goes a long way and don't put it on everything. For the drums usually the overheads are enough to get you going, the vocals to smooth/thicken them (but keep them sounding close by) and maybe 5-6% on stuff like synths or guitars should be good.
Once you have levels set, your stereo panorama staged, things are EQ'd and sounding crisp and purposeful, and you've applied any special effects like reverb... you combine all those elements into a 2 channel stereo MIX (2 channels--one for right, one for left).
Mixing can be a lot of fun and is my favorite part of the recording game--provided you were given decent tracks to work with. Nothing is more irritating than to be told that YOU have to fix the band's sloppy timing errors and so forth. You can usually do it, depending on the mistake, but the best bet is to provide the mixer with as perfect a recording as possible to work on.
"Fix it in the mix" is a nice way of saying "polish that turd later."
MASTERING: now that the mix is done it's time to master. Mastering is the process where you put the final finishing touches on a recording.
Not all mastering has to do directly with sound, which is why a lot of people find mastering to be a bit confusing.
The best way to understand mastering is too look at not a single recording or song but a *collection* of them (as an example, all the songs for an album). The mastering engineer's job is to make these songs all sound similar to one another as far as overall frequency spectrum and volume--imagine if you had an album where one song is 6db quieter than the others, and another song had three times as much bass, and another one tons of mids... and so forth--it would make for a really annoying album to listen to because you'd constantly be adjusting your stereo.
The mastering engineer will make sure that the songs play together as a collection of songs well. They will also check how the songs perform on other types of speakers such as portable radios, car stereos and try to reach a compromise where the different formats sound very similar and good.
Mastering houses will also fix whatever problems that occured in the mix as best they are able--such as if the mix has just too much high end or not enough bass. Unfortunately if you need to take down a single instrument it is often impossible to do so at the stage; your best bet is to remix. Mastering is powerful but it can't work miracles. Phase issues between stereo sides will get rectified here in case the mixer missed that.
"Fix it in the master" is another way of saying "polish that turd later."
During mastering you also choose a SONG ORDER that determines which track goes first, what's second, last song... and so forth. They will place the CD locator points for those songs and any silences (or lack thereof) that the artist requests.
Also, a good mastering engineer will attempt to make a high quality, redbook master CD for duplication--insuring that the recordings meet the technical requirements of mass production. This is a critical step for artists that are reproducing their audio for sale.