A Straight is a five-card hand with five sequential cards: starting with the lowest card and ending with the highest card, each card is incremented by one.
Most Straights are made in later rounds of betting, after chasing a draw. This usually means you either check to get more cards dealt or call bets that are sized according to your odds of making your draw: you only call if you're likely to make the straight and then the bet is reasonably sized compared to the pot.
There are multiple types of straight draws.
One is the up-and-down: you have four cards to the straight, and could make it with either the card below your lowest card or the card above your highest. For example, you hold a 6, 7, 8, and 9--so either a 5 or a 10 will make your hand. This is the strongest kind of straight draw, because you have the most outs: eight cards could make your straight.
There's also a gutshot, or belly-buster, draw: you hold four to a straight but are missing one in the middle. For example, a hand with a 9, 10, Queen, and King is a gutshot draw to a straight--a Jack would make it. A gutshot is not as strong as an up-and-down, because there are only four cards to make the Straight.
What's more, a Straight can be beaten by a higher straight: another player might have a better straight using the same community cards as you. If you have the lowest possible straight using the community cards (for example, you hold a 4 and 5, and the board shows 6, 7, and 8), you have what's called the ass-end, and you could be beaten.
But if you know your straight is strong (such as the nut straight), then you can concentrate on building the pot. You want to earn calls or elicit bets from aggressive opponents.
A Straight is described as "to" the highest card--so a Straight of 7, 8, 9, 10, and Jack is "to the Jack." And the player with the highest card wins, so a Straight to the Jack beats a Straight to the 8.
If two players have the same straight, they split the pot.
Most games treat the Ace as high or low, so that Ace, 2, 3, 4 and 5 is the lowest Straight and 10, Jack, Queen, King, Ace is the highest. But some players--usually home game players--use wraparound straights: the Ace plays high and low, so a player could have a Straight of King, Queen, Ace, 2, and 3.
This is almost never the case in a casino, so don't look like the amateur at the card table by trying to play a wraparound straight!