Basically the idea is that there is a bitterness to some eggplants (and I think this is particularly true of the commercial varieties that have been shipped from afar) and that this bitterness can be purged by salting the eggplant. You can do the salting either by pouring vast quantities of salt over your sliced or cubed eggplant, or by soaking the sliced or cubed eggplant in very salty water. I usually opt for the latter. At any rate, you allow the salt to penetrate the eggplant for 30 mins, and then rinse all the salt out, and with it the bitter eggplant juice. You can actually see a dark liquid that leaves the eggplant after salting via either method. It's very traditional to start by processing eggplant in this way--most recipes advise it.
My claim is that eggplant is never bitter, in my experience, and therefore the salting is an old wives tale and a total waste of time.
However, I seem to be a class of 1, on this one. Everyone in the universe salts their eggplant. (My indian, french, middle eastern and american cookbooks ALL call for salting eggplant.)
edited to add
Oh! I just remembered this! Another reason to salt eggplant is to stop it from being so darn absorbent. You can throw oil at eggplant all day long, and it will just keep on soaking it up. I believe that the salting--and subsequent use of water--helps to stop the eggplant from being such an oil-lover. However, I have learned to cook eggplant with just the teensiest bit of cooking spray (and other non-fat liquids), so this isn't really a problem for me.
That said, one of my favorite eggplant recipes is to cube it, marinate it with a ton of ground spices (cumin, coriander, tumeric, cayenne, salt, pepper, etc) and then fry it in oil. It's delicious. I make a sweet and sour tomato chutney that goes
perfectly with this indian style fried eggplant. Not friendly to the dieter, of course, so I haven't prepared eggplant this way in eons. But it is good!