The gist of Dominion is that everyone starts out with 10 cards; 3 "victory point" cards, and 7 money cards. Available to buy with your money cards are money cards in higher denominations, more victory cards, and 10 different types of "action cards". When you buy cards, they go in your discard pile, as do the money cards you spent to buy them, and the entire rest of your hand. When your deck runs out, you immediately shuffle your discard pile and turn it into your deck, so as you play you're building a deck tuned to whatever strategy you want to use. At the end of the game, whoever has the most victory points wins, but victory point cards are dead weight otherwise, so you have to strike a balance between having enough to win but not so many that you clog up your deck with them.
This game is also incredibly "elegant". There are no cards that "stay out" on the table, so you never have any cards in front of you except when it's your turn and you're showing the other players the cards you're using that turn; otherwise everything stays in your hand, your deck, and your discard pile. Also, the game runs a lot faster than you'd expect it to, since the next player starts his turn while you're discarding the cards you've used that turn, shuffling your discards if your deck has run out, and drawing your new hand, so when play comes back to you you've already had time to look at your hand and you already know what you're going to do.
The 10 types of "action" cards that I mentioned in the beginning are pulled from a pool of 25, so not only are there multiple strategies for whatever set of 10 action cards are available, but there are also tons of different possible combinations of 10 action cards. The rules suggest three different "themed" sets of 10, but they also encourage you to make up your own sets, or choose the set randomly, or democratically, or however you want. There are also expansions for the game that add EVEN MORE possibilities, but I think we'll stick with just the core game for a LONG time before we exhaust all the possible combinations and strategies and start to crave more variety.
Based on the three games we played of this last night, this is far and away my absolute favorite tabletop game EVAR, and I very highly recommend it.