Zeus swallowed Metis to prevent the prophecy of her future son overthrowing him from being fulfilled, but she was already pregnant, and later her daughter Athena sprang from Zeus' head. What happened to Metis herself when this happened?
There are two possibilities here:
Either, Metis was killed when Zeus swallowed her:
It may seem odd for Metis to have been pregnant with Athena but, never mentioned as her mother. This is because the classic Greeks believed that children were generated solely from the fathers sperm. The women was thought to be nothing more than a vessel for the fetus to grow in. Since Metis was killed well before Athena's birth her role doesn't count.
However, other myths state that she continues to live inside Zeus and that she is the source of Zeus' wisdom. Since she was the goddess of wisdom, prudence and deep thought:
It is said that she is the source for Zeus wisdom and that she still advises Zeus from his belly.
I believe the second is more believable because Zeus is himself titled Mêtieta, "the wise counsellor," in the Homeric poems and the Wikipedia article for Metis also states that (while she was inside Zeus):
She began making a helmet and robe for her fetal daughter. The hammering as she made the helmet caused Zeus great pain.
Which would mean that Metis was not killed and was living inside Zeus.
Athena becomes goddess of Wisdom, Skill and Craft.
- The myth is about the transformation of the titanic aspect of the former generation into the present incarnation under the new Olympian order
Logic's answer is solid, but arises out of the patriarchal viewpoint. A part of Metis might stay in Zeus and give him wisdom—Odin literally drinks Kvasir's blood to gain his power.
But in a deeper sense, Metis becomes Athena, who now operates within the structure of civilization.