PC recording software comes in many different types and capabilities.  What I want to focus on here is software you can use to record music or voice overs onto your computer.  That narrows it down to two categories of audio recording software: programs to use for “tracking” or getting the sound into the computer, and programs used for editing audio after it has been recorded.

Audio Tracking Software

First off I should mention that there is considerable overlap between the two kinds of software I am describing, but the main difference is that one is primarily used to record the sound (music, voice over, etc.), and the other is primarily used to change the audio in some way, usually by altering the actual audio file (destructive editing).  For audio tracking (our first type of software) you will absolutely want the ability to multitrack.  What I mean by this is that you need to be able to record one thing on one track (say, an acoustic guitar), a second thing (say, a singer’s voice) on a second track that will play back AT THE SAME TIME as the first track, etc.  If a tracking program is capable of multitrack recording, the number of tracks you can create (remember…all playing back at the same time) is usually unlimited for all intents and purposes.  That means you’ll be able to do some very cool things like record yourself singing harmony with yourself (a quartet or entire choir!), add guitar, drums, piano, etc. and be a one-person band.  This is truly the killer app for computer recording.
In the old days (like in the 90s and before….so yeah, not THAT old), it was difficult and expensive to do multitrack recording.  When using audio tape, the professionals used tape so wide, usually two inches, and moving so fast through a recording machine (usually 15 inches per second) that there was minimal noise and maximum audio quality.  Consumers were left with two choices, pay to rent time at a commercial studio, or buy a machine yourself.  Regular people could typically only afford multi-track cassette recorders whose maximum track count was usually 4 because cassette tapes were so narrow.  Because of the limitations, audio quality was not terrific coming from these consumer multitrackers.
So maybe you can imagine why it is such a big deal that software allows good audio quality and unlimited track count!  Anyway, audio tracking programs are frequently referred to as digital audio workstations (DAWS).  You “lay down” (record) one track, then another, then another, etc. until you’ve recorded all you need.  Then you pan each track to make it sound like it’s coming from the left side of the listener, the right side, or the middle.  You might also want to put some effects on each track to get them to sound just right.  When you’re done with all that you mix all the tracks down into a stereo file.  Nowadays this is also called rendering.

Audio Editing Software

Like I said, there is significant overlap between these two types of audio program.  For example, most editors can also record audio as well.  But you usually can’t do multitrack recording with an editor.  For the purpose of this article, I want to focus on the editor’s use once multiple tracks have been mixed down/rendered to a single file.  Sometimes this is called mastering.  Though in truth, audio editors have many other uses.
So after you’ve mixed all your audio tracks and files down to one final stereo sound file in your DAW, you’re ready to use your editing software.  The main difference now is that you’re working on how one single file sounds, rather than how a bunch of different bits of audio sound, alone and together with the other bits of audio.  That is such a big mindset difference that in the music business it is common for different people entirely to do each job.  For most home recording projects though, we frequently end up doing both jobs.
You open the file in the editing program and turn it into a final product by slicing, fading, turning up, turning down, and other actions that change the audio in some way.  For example, if I were doing the final edits for a song, I would make sure any extraneous noise at the beginning and end of the song are cut out, and that the song starts and ends smoothly.  Sometimes there’s a count-in, or someone coughing just at the start or end.  An editor can slice that right off.
Next you’ll want to pay attention to loudness.  In order to get the entire song loud enough, you may need to turn parts of the song down before you can increase the average loudness of the file.  You can read more about this process of compressing or limiting audio in another article on the Home Brew Audio site.
Other things you can do in the final editing stage is filter out parts of the song that may be too loud, like certain bass frequencies, or SSS sounds, etc.  Then you might want to add some effects like echo or reverb.
When you’ve finished editing your song, you save it in the editing program as a single stereo file (though it could be mono or even surround these days).  Now the audio is ready to use in any way you see fit.
Examples of tracking software, or DAWS are: Reaper, Pro Tools, and Cakewalk Sonar.  Popular editors include Audacity, Adobe Audition and Sound Forge.
So as a review, there are two main varieties of audio software, tracking programs and editing programs.  You use the first type to record all the different audio onto tracks, apply track effects and mix all the tracks together to create one single audio file.  Then you open the file in your editor and snip, stretch, massage, squash and polish it until it sounds just right, and you save it as the final product.  Believe it or not, that is a nutshell version of audio production in general:).