An idiom is a form of expression that is particular to a certain person or group of people. If your friend always says, "squirrelly nuteriffic!" when she means something is great, she's using her own idiom.
Idiom comes from the Greek idios, which means personal. Idiom originally meant "speech peculiar or proper to a people or country." These days we use idiom for a specialized vocabulary or an expression that isn't obvious, like kick the bucket which means "die." If you're studying a foreign language, idioms are the hardest phrases to translate.