There are a couple reasons you might use an external mixer:
1) Most commonly, a DAW user will have an external mixer to use its many and inexpensive preamps. Mics have to be plugged into some kind of preamp before they go into the computer and a mixer is generally the cheapest way to get a few decent sounding pres.
2) WHAT DID YOU SAY?! HOLD ON A SEC (fumble with mouse) LET ME (fumble, fumble) TURN DOWN MY COMPUTER!!! (Fumble, fumble.)
If you have a mixer, its often a very convenient way to control the volume of your monitors. Plug the outputs of your computer into a input on the mixer and plug your monitors into the main outs of the mixer. Voila! The master fader (and channel mute switches) can be used to quickly and easily control your system volume.
3) Mixing.
Less often in home studios, but very commonly in pro studios, individual tracks are sent out multirack audio interfaces to the individual mixer inputs and mixed on the analog mixing board like the days before computers. In this case the DAW is acting llike a multi-track tape deck with benefits: editing and automation can still be done on the computer and you can still use your plugs as inserts. Most folks who go this route also have analog compressors and effects that make it more worth doing, as well.
That's the basics of it.
Take care,
Chris
