Cardinal numbers (i.e. one, 7, four, three, etc) tells "how many." Cardinal numbers are also known as "counting numbers," because they show quantity. Here are some examples using cardinal numbers: 8 puppies, 14 friends.
Ordinal numbers (i.e. first, 2nd, third, 4th, etc) tell the order of things in a set. Ordinal numbers do not show quantity. They only show rank or position. Here are some examples using ordinal numbers: 3rd fastest, 6th in line.
Nominal numbers names something—a telephone number, a player on a team. Nominal numbers do not show quantity or rank. They are used only to identify something. Here are some examples using nominal numbers: jersey number 4, zip code 02116.
Source