This one is pretty much self-explanatory. A win bet means you are betting on a horse to win the race. It is possible to bet multiple horses to win (though of course only one can actually win, unless there’s a dead-heat) and there is typically a $2 minimum bet. This is the bread and butter of any serious or casual bettor.
In order to cash a place bet, your horse must finish in either first or second. The payout will be the same regardless of where they finish (so long as it’s in the top two), and like a win bet there is typically a $2 minimum.
A show bet pays dividends if the horse you wager on finishes in one of the top three positions. Same as a place bet, whether the horse finishes in first, second, or third makes no impact on the payout. If your horse is anywhere in the top three, you win.