An MOT is a required test that your vehicle has to pass in order to demonstrate its roadworthiness. Once your vehicle is at least 3 years old, it needs to pass an MOT every year. This involves a pre-determined series of tests that your car has to pass.
A service is different, and isn't required by law. While an MOT tests roadworthiness, a service goes a bit further to check that everything is running well, rather than just that it is running at all.