Agile testing generally means the practice of testing software within the context of an agile workflow.
When testing in an Agile way, there are few, if any, rigid adherence's to requirements documents and checklists. The goal, instead, is to simply do whatever is necessary at any moment to satisfy a customer’s requests, replacing documentation with in-person meetings and replacing siloed functions with unified, self-organizing project teams.
In an Agile company culture, everyone is expected to work closely together, no matter his or her role, to achieve a single goal: a high-quality software product that fulfills all of the essential specifications a client or designer requires with each iteration. Software developers, testers, and quality-assurance personnel wear each others hats from time to time, and while there may be a select group of people running most of the tests, the notion of a separate testing team disappears entirely for many product teams, and disappears within the core development cycle for those organizations who are required by external agencies (or even by law) to have formal and/or external release candidate testing. Even in these cases, this separate release candidate “testing” isn’t testing for the purpose of finding problems or improving the product, it’s an exercise in verification, regulatory compliance, and/or audit trail completion.