An audible is simply a last-second change to the play, called by the quarterback, when the offense is already lined up at the line of scrimmage. This usually occurs when the quarterback sees the defense's formation or detects a possible blitz and determines that the original play call would likely be unsuccessful.
For instance, if the quarterback is under center and sees potential blitzers and feels he can likely not get the pass off and completed, he could option to a pre-determined run play by giving a code word or sign to the other players on his team. Each offensive play has a built-in audible option, so everyone on the team is on the same page when the signal is given.
The Denver Broncos' quarterback, Peyton Manning is popular for his codes and signals at the line, famously yelling "Omaha" last season and gaining national attention for his consistent use of the term.
Often times, when a quarterback predicts a blitz, he will make a signal to one or more of his receivers. This is called a "hot route." It tells the receiver to adjust their predetermined route to a shorter route like a slant or screen. This adjusted route gives him a quick place to throw the ball and avoid taking a sack or loss of yardage. If no blitz comes, the rest of his receivers are still running their normal patterns.