An AsyncTask is not tied to the life cycle of the Activity that contains it. So, for example, if you start an AsyncTask inside an Activity and the user rotates the device, the Activity will be destroyed (and a new Activity instance will be created) but the AsyncTask will not die but instead goes on living until it completes.
Then, when the AsyncTask does complete, rather than updating the UI of the new Activity, it updates the former instance of the Activity (i.e., the one in which it was created but that is not displayed anymore!). This can lead to an Exception (of the type java.lang.IllegalArgumentException: View not attached to window manager if you use, for instance, findViewById to retrieve a view inside the Activity).
There's also the potential for this to result in a memory leak since the AsyncTask maintains a reference to the Activty, which prevents the Activity from being garbage collected as long as the AsyncTask remains alive.
For these reasons, using AsyncTasks for long-running background tasks is generally a bad idea . Rather, for long-running background tasks, a different mechanism (such as a service) should be employed.
An activity is typically a single, focused operation that a user can perform (such as dial a number, take a picture, send an email, view a map, etc.). Yet at the same time, there is nothing that precludes a developer from creating an activity that is arbitrarily complex.
Activity implementations can optionally make use of the Fragment class for purposes such as producing more modular code, building more sophisticated user interfaces for larger screens, helping scale applications between small and large screens, and so on. Multiple fragments can be combined within a single activity and, conversely, the same fragment can often be reused across multiple activities. This structure is largely intended to foster code reuse and facilitate economies of scale.
A fragment is essentially a modular section of an activity, with its own lifecycle and input events, and which can be added or removed at will. It is important to remember, though, that a fragment's lifecycle is directly affected by its host activity's lifecycle; i.e., when the activity is paused, so are all fragments in it, and when the activity is destroyed, so are all of its fragments.