A small test that makes sure a certain unit of your codebase works as intended. They have the smallest and narrowest scope of all your tests which result in very quick run times. What is a unit? It depends on your context.
Here's an example from Martin Fowler: "If you're working in a functional language a unit will most likely be a single function. Your unit tests will call a function with different parameters and ensure that it returns the expected values. In an object-oriented language a unit can range from a single method to an entire class." Martin Fowler
Test Doubles replace a real thing with a fake thing, returning a canned response instead (that you specify ahead of time in your test).
Dummies: objects are passed around but never actually used. Usually they are just used to fill parameter lists.
Fakes: objects actually have working implementations, but usually take some shortcut which makes them not suitable for production (an InMemoryTestDatabase is a good example).
Mocks: are pre-programmed with expectations which form a specification of the calls they are expected to receive. They can throw an exception if they receive a call they don't expect and are checked during verification to ensure they got all the calls they were expecting.
Spies: are stubs that also record some information based on how they were called. One form of this might be an email service that records how many messages it was sent.
Stubs: provide canned answers to calls made during the test, usually not responding at all to anything outside what's programmed in for the test.
Definitions from Martin Fowler