Why does Hrothgar ask Beowulf to battle Grendel's mother, and what does Beowulf do after he kills her?

Grendel's mother is grieving for the loss of her son, so she seeks revenge and attacks Herot.  Hrothgar's closest friend is carried off by her into her deep underground/water lair.  Along with his friend, Grendel's arm that was hung in Herot Hall was taken by her back to her dwelling.

Hrothgar goes to Beowulf and asks for help again in exchange for riches.

"Our only help, again, lies with you...Save us, once more, and again twisted gold, heaped-up ancient treasure, will reward you for the battle you win!"

Once he battles her, he kills her by chopping off her head.  He then follows the hall to where the dead Grendel lies and chops off his head, too.  He then takes Grendel's head back to Hrothgar and receives his riches.