There are a heap of them, but Magic has I think a 90% market share. Basically, they are complex card games, save that you play with special cards. Additionally, a card can have text on it which describes a special rule or condition which is valid while the card is in play or an effect it causes by being played. This can even contradict the game rules (the card takes precedence). There are literally thousands of different Magic cards, each with its own unique effects, so you have to build a deck which attempts to combine effects or to use the most powerful ones to give you an edge. Games are fairly fun and unpredictable at amateur level. Pros, OTOH, only play with the two or three most powerful strategies available at the moment (since expansions roll out constantly, the strategies change over time).
Since you find cards at random in packs, players trade them to get what they need to build their deck. And since not all cards are being printed at any given time, and some aren't going to be reprinted any time soon, hardcore players often lust after out-of-print cards.
TCGs can be fairly addictive and fairly expensive, but they're better than tobacco. Top-notch players can even gain some money out of it (usually by screwing newbies out of all their rares, and then selling them for outrageous prices).