This is a slang term for a professional gambler. A sharp will typically be very good at handicapping and may specialize in betting on one or more sports.
A sharp is known as such because they are smart, or "sharp," when placing wagers. These people typically have a lot of disposable income or use betting on sports as a primary means of income. A sharp is the type of person a professional linemaker or bookie will go to if they want to offer someone an outlaw line. There are more professional gamblers these days because computers make it much easier to calculate odds of winning, and to place bets according to those odds. Professionals will calculate their own odds and then try to find the point spread or odds which best fits their prediction. A sharp may also be referred to as a wiseguy.