O'Reilly has a great in-depth article on the functional interface in Java 8. Here's a quick cheat sheet to keep track of the main types, what they do and common use cases.

Predicate

A Predicate returns true or false. These are used for filters or replacing big chains of if/else logic.

Function

A Function transforms data. These are used for maps, and other transformations. It is important to not mutate the original data that is passed in.

Supplier

A Supplier takes no arguments and returns a value of a known type. Fetching, reading or creating resources to be used by other functions are common use cases. Suppliers get things started.

Consumer

A Consumer accepts a single argument, but does not return any results. Consumers are where mutating functions, things with side-effects, should go. Consumers finish things.