Google introduced fragments when they lunched Honeycomb (3.0).
As you may know, Honeycomb was the first Android version to support tablets out-of-the-box and they use fragments to better arrange UI layouts on the screen.
With Fragments you can utilize screen property way better then with activities. One activity can run and "command" many different fragments that share same screen real-estate and the fragments can be swapped on the fly.
So yes, Google WANTS you to use fragments and it is the right way to write most scale-able applications.
As for the second question:
Fragments can persist across configuration changes - like screen orientation changes for instance. Activities gets killed and recreated when you change screen orientation and any work they might do will have to be recreated again.
If you use fragments right, then when you change screen orientation the activity might get killed but the fragment can persist its state and then re-attach itself to the newly created activity and continue where it left.
Basically, if you have an AsyncTask running from an activity and the activity gets killed because of orientation change (for example), you AsyncTask is useless now. But if you hold the AsyncTask through a fragment then it will continue because the fragment isn't destroyed.
Hope this helps