Acceptance tests are a great tool to verify that the application or system works as expected from end to end. Sometimes these tests can be called end-to-end tests but sometimes end-to-end tests have a different meaning. Another term to describe the same functionality is QA tests and a subset of acceptance tests is often referred to as smoke tests.
The Idea
The idea is to define input and the expected output and once the system and all its dependant services are running the whole system can be verified to work as expected. In an ideal world, the acceptance tests would be implemented based on the acceptance criteria of the use case.