It would be helpful if you told us what mixer you have...
That said, it's pretty basic. The main outs are just that, the MAIN outputs. These would be your stereo outputs. You can use them to feed your monitor speakers (if they're powered, that is) or you could patch them into the inputs on your soundcard. Where you route them depends on your equipment and setup, neither of which you described. Alt 3/4 are sub outputs, depending on your mixer, you could 4 or 8 of these. If you look at each channel, there is probably a switch that allows you to route each channel to either the 1/2 or 3/4 bus (assuming you have a 4 bus mixer) , these, in turn, are sent to your main outs. This gives you the added flexibility of routing some signals, say for a cue (headphone) mix or possibly to an outboard processor or, if you connect your sub outs to your soundcard, (assuming it has more than a stereo input), you could assign each sub to its own track in your recording software.
A mixer is all about flexibility. The more options a mixer offers for signal routing, the better.
Tell us more about your setup and if you are trying to accomplish something specific or have a problem. We'll do a lot better with more information.
Another suggestion, READ! Not to be rude, but the information I'm giving you and probably quite a bit more will be found in the manual for your mixer.
Good luck.
Ted