Dominion is a popular deck building game, one of the first board games to be based on this mechanic, coming out way back in 2008. It was designed by Donald X. Vaccarino, and originally published by Rio Grande Games.
It is not too different from the average deckbuilder. You start with a small set of cards representing copper pieces and victory points, and use these copper pieces to buy better cards, including coins worth more, cards that are worth more than 1 vp, and best of all, cards that do things like allow you to draw extra cards, steal cards from other players, curse other players, protect yourself from other players, and so forth.
Unlike many deckbuilders, Dominion has a stable card bank. That is, if you buy a 'Festival' card, it is not replaced by a random card but by another Festival. This allows for long-term strategizing in a much more concrete way than is possible in most deckbuilders. Moreover, you choose what the card bank looks like; the base game comes with 25 sets of 'kingdom cards', and for each game you choose only ten sets to play with. This allows for games to be highly variable, resulting in more replayability and gives the players more control in choosing the type gameplay they want.
Dominion also has an unusual mechanic in that you are limited in both actions (playing a kingdom card) and purchases for each turn. You can, and should, buy cards that give you more than the default one action and purchase per turn, but this is often a slow process that can be hard to balance. Very few deckbuilders have opted for such severe restrictions on play, but it works well as long as you use some common sense in choosing your kingdom cards when setting up the game. If in doubt, the rule booklet provides recommended setups.
Having been around for a while, and being quite popular, Dominion has a lot of expansions -- there are currently 10. Additionally, in 2016 the base game was modified from the original, removing six of the original kingdom cards but adding seven new ones. Additionally additionally, some expansions can be played as stand-alone games or added to the base game as you choose, while others are only playable if you have the base game (or a stand-alone expansion) already; some have been released in both stand-alone and non-stand-alone formats. (There is also a small set called Base Cards which is not the base game).
But don't worry about all of that. It's a good game, and if a friend offers to teach it to you, take them up on the offer. I wouldn't necessarily recommend Dominion as a game to purchase without trying it first, as it is a bit expensive for a deckbuilder (it is currently selling at $30.00 on Amazon, although the SMRP is $45). It is worth the price if you like it, but in my experience people often prefer the newer deckbuilders. It would make sense, if you are buying before playing, to start with a cheaper starter set of a popular deckbuilder, such as Star Realms or Ascension: Apprentice Edition.
Dominion has won a number of awards, including: the 2010 Games Magazine Best New Family Strategy Game, the 2009 Mensa Select, the 2009 Golden Geek Board Game of the Year and the 2009 Golden Geek Best Card Game, the 2008 Meeples' Choice Award, and just about every European gaming award there is, from the Hra Roku to the Årets Spill.