Here it is: the big one. A Royal Flush is a five-card hand containing the 10, Jack, Queen, King, and Ace of a single suit. It's very rare, but if you have it, you're usually guaranteed to win the pot--assuming you are able to get anyone to call.
Most poker games don't start with five cards being dealt at once, which means most Royal Flushes start as draws: you'll have two or three of the cards needed, and get the others dealt during a later round of betting.
A Royal Flush is a rare hand, which means you should never bet on getting one--even if you have four out of the five cards, chances are you won't make the Royal Flush. But, four of the five cards to a Royal Flush is still a strong hand to bet on, since you can still hit a straight or a flush, or even a straight flush to the King. That said, pay attention to your opponents: if someone else has a made hand, and you're chasing the Royal Flush, you might not want to invest too much on that draw.
One of the tough things about a Royal Flush is that it's almost too strong: chances are your opponent is going to be scared away by all those suited connectors on the board. So you want to consider how to best build the pot: should you slowplay the hand, with the hopes your opponent makes a play, or should you bet big so they think you're bluffing? Either way, a Royal Flush is all about eliciting calls from players who won't know what hit them.
In the rare instance two players hit a Royal Flush, they would split the pot.
In games with wild cards, it's possible to get Five of a Kind: a five-card hand containing five cards of the same rank. In many games, this is considered the best hand, and even beats the Royal Flush. Other times, Five of a Kind beats all Straight Flushes except the Royal Flush. Always know the rules of the game you're playing.