Agile testing is a software testing practice that follows the rules of the agile manifesto, treating software development as the customer of testing.
Agile testing involves testing from the customer perspective as early as possible, testing early and often as code becomes available and stable enough from module/unit level testing.
Since working increments of the software is released very often in agile software development there is also a need to test often. This is often done by using automated acceptance testing to minimize the amount of manual labor. Doing only manual testing in agile development would likely result in either buggy software or slipping schedules because it would most often not be possible to test the whole software manually before every release.