A lay bet is essentially the opposite of a traditional bet, with the punter taking the position of the bookmaker, saying that an outcome won’t happen. With this form of betting you run the risk of having to pay out should your prediction be incorrect, making it a bet for more experienced punters and not for the risk-averse.
There are a range of different outcomes which can be bet against, offering various odds. With football and most sports, this tends to be simply whether a team will lose, or someone won’t score a goal. In horse racing betting the options are much more diverse, with punters being able to say a horse won’t finish first, last, place, not place, etc.