Testflight is Apple's own beta testing software that allows developers to test their apps with a group of internal testers. Developers are able to upload beta builds of their apps, with new interfaces, new features, etc to have feedback of other users before uploading to the App Store.
Apple had placed a limit of 1,000 testers per developer, and each build could be valid for 30 days, but that recently doubled. Developers are now able to add up to 2,000 testers, and each build will now work for 60 days. When Apple announces new versions of iOS during its Developer Conference, it doesn't allow developers to add features from the new versions to its App Store apps until usually around September.
During these times, and year round, developers are able to take advantage of Testflight to have others try their apps. Installing an app through Testflight is dead simple. The developer adds your email address, then you download the Testflight app, and the apps you are a tester for show up.
Recently, Testflight has added push notifications to notify you when new builds are available, and it now also displays change logs so developers can easily communicate with testers what to be on the lookout for.