When players talk about "limit poker" (also called "fixed limit") they refer to a style of betting where the bets are of a specified size. For instance, a draw poker game may have limits of "$2/$4", meaning that before the draw, all bets go in increments of $2: The first player bets $2, the second player raises $2 to $4, the third player raises $2 to $6, etc. After the draw, the bets have doubled to $4: First player bets $4, the second player raises $4 to $8, and so on. Every bet must be precisely $2 before the draw, and precisely $4 after the draw, not more and not less. The only exception occurs when someone is all-in, at which point other rules kick in for what happens - these rules are/can be different for different cardrooms, so that's typically something you need to investigate yourself. The basic principle is that a side-pot is created that the remaining players (that are not all-in) will compete for.
In a fixed limit game, one talks about "small bets" and "big bets" when referring to the different bet sizes, online often written as "SB" and "BB" (and they both cause some confusion as they share acronyms with the Small Blind and Big Blind respectively - be aware of that).
For hold 'em - where there are four betting rounds - a $5/$10 limit game the structure means that the first two betting rounds with small bets (preflop and flop) are in increments of $5, and the final two with big bets (turn and river) are in increments of $10. Different real money poker sites (and casinos, for that matter) have different rules regarding the maximum number of bets that can go in on any round, but the norm is 4. This means that the most you can possibly lose in one hand of $.50/$1 limit hold'em with four bets maximum per round is 4SB + 4SB + 4BB + 4BB, or $2 + $2 + $4 + $4 = $12. The way this limits the potential losses is what makes many feel that limit is "safer." Don't let this fool you, though - learning how to perfect your limit game is a never-ending process, just as it is with no-limit or pot-limit. The skill sets are different, but anyone saying that limit takes no skill is likely just frustrated from running bad. Some sites have special rules for betting when the hand becomes heads-up: they don't have a cap for how many bets can go in. So heads-up on the river two people may (at these sites) raise and re-raise each other until one of them is all-in. Of course, either of the players can stop raising and just call at any point they like. This type of non-cap is not the norm, however, but it may be good to be aware of (as a sidenote, the primary reason it is only allowed when the pot becomes heads-up is because it makes it impossible to use as a tool for colluders, or people who team up and try to bet and raise a better hand out of the pot - and splitting the profits. This type of play is of course cheating, and colluders will be dealt with harshly).
The options at a limit poker table: Fold, call or raise.
For learning the basics of the game of poker, limit is almost always the best way to start. Contrary to what you may think, however, I don't recommend beginners to start with limit because the losses are limited (make no mistake - you can go bust at a limit table as well, and there are plenty of sharks around who would love to help you with that). No, I recommend to start with limit because it gives you a chance to focus on game rather than trying to figure out how much to bet. In limit, you only need to ask yourself "what" to do, and not worry about "how much." The concepts of pot odds and implied odds, for instance, are important in all forms of poker, but are much easier to practise calculating in a limit game.
Don't make the mistake of thinking that limit is a simple game, because of this. Learning the finer points of the game requries a lot of studying and a lot of practise. Fortunately, limit is one of the few areas of poker where there - at the time of writing - are a lot of great books available. This is sadly not the case for pot-limit and no-limit, where the focus (for some reason) seems to be with tournaments rather than cash games. See the studying section for some tips on books to pick up.