Idiom - a phrase with a hidden meaning, the phrase doesn't actually mean what it says. An example would be "you're in the doghouse." If you take this statement literally, you can picture yourself sitting inside a doghouse. However, it actually means that you are in trouble. Another example would be "when pigs fly." Literally it means that pigs have wings and they are flying, however actually it means that someone is telling you "never."
Proverb - a popular saying that states something wise and/or truthful. An example would be "an apple a day keeps the doctor away." This is a popular saying that nearly everyone in America has heard. It is a wise saying that has been passed on from generation to generation. Another example would be "If you can't beat 'em, join 'em." This is another popular, yet truthful saying. When you think of proverbs, try thinking of all the "old school" statements that your parents told you when you were a kid: "treat others the way you want to be treated," "it takes one to know one," "misery loves company."
Hopefully this will help you see the difference between idioms and proverbs.