There are different kinds of betting limits in poker. In a no-limit game, usually a very high-stakes game like the World Series of Poker, there are no rules governing the amount that a player can bet or raise.
The most common limits are fixed-limit games. A fixed-limit poker game is identified by two betting amounts and the type of game. For example, an online poker site might host $5-$10 Texas Hold'em tables. That means that for the first few rounds of betting, each bet must be an increment of $5. If someone bets $5, you can only call that bet or raise it another $5. At a certain point (depending on the game), the betting limit doubles; all bets are then made in increments of $10. Most casinos limit the number of raises in a single betting round to three or four.
Some games use a spread limit, like $1-$10. That means a bet can be any value between the limits, but each raise must be at least as much as the previous bet.
Finally, there are pot-limit games. In these games, the betting limit is the amount currently in the pot, including your current call. In other words, if there is $20 in the pot, and the player before you bet $10, you can raise up to $40 ($20 in the pot + $10 bet + $10 call).
A term you might hear often around a poker game is "table stakes." "Table stakes" simply means you can only play with the chips you have on the table. If you tap out (run out of chips), you can't buy more in the middle of a hand, or pull a $20 bill out of your pocket to play with. You have to leave the table at the end of the hand, buy more chips, and then return to the table when a new hand is beginning.