WIN
You pick the horse that finishes first.

PLACE
You pick the horse that finishes first or second.

SHOW
You pick the horse that finishes first, second, or third.

Daily Double
   You pick the winner of two consecutive races.

Exacta (or Perfecta)
    You pick the first two horses to cross the finish line in exact order in a single race.

Exacta Box (Also called a Quinella)
    You pick the first two horses to cross the finish line in either order in a single race.

Pick Six
    A type of wager in which the winners of all the included races must be selected. 

Trifecta
    You pick the first three horses to cross the finish line in exact order in a single race.

Trifecta Box
    You pick the first three horses to cross the finish line in any order in a single race.