This is slang for a money line wager on a favorite in a money line event (as opposed to a point spread event). A money line will list how much one will win if they wagered $100.
Laying the price is popular in the NFL because money lines are popular when placing bets on NFL games. A typical matchup will look something like this: New Orleans Saints (+120) vs. New York Giants (-110). In this case, the New York Giants are the favorite and in order to win $100, the bettor must put down $110. A wager on the New York Giants means the bettor is laying the price. This phrase is very similar in meaning to "lay the points," as both refer to betting on the favorite. In some cases, laying the price can be very expensive, especially if the team is favored heavily. The most profitable times to lay the price is when the difference between the prices is at a minimum.