Here's how they work (though the post above is pretty close!)
Instead of buying an entire condo, you get a "share" of it to use every year. Most timeshares now, instead of giving you a specific week, give you points to use. If used properly, you could get between 15-25 days a year at various timeshares around the world during off-peak season.
However, here is the problem with timeshares:
You are totally dependent on their availability, like a hotel. And you pay ever increasing "maintenance fees" every year - this covers your share of the taxes, insurance, utilities, staff wages, etc.
If you have a family, like to vacation a lot, go to different places, or know when every year you will vacation, then it might work out for you. Better than staying in a small hotel room, as you will get a condo with a kitchen, etc.
However, the best deals out there are the timeshare resales - pennies on the dollar, and no bullshit high-pressure sales crap.