Acceptance test verifies scenarios from a user's perspective. The application tested is accessed via either PhpBrowser or a real browser. In both cases the browsers are communicating via HTTP so application should be served via web server.
Acceptance testing is implemented with the help of Codeception framework which has a nice documentation about it:
If you've started with advanced template, please refer to "testing" guide for more details about running tests.
If you've started with basic template, check its README "testing" section.