To live as a loner, by choice or not, despite the presence of other options; for spiritual reasons or other reasons; to spend time away from people to read, write, introspect, gain knowledge, learn about self, learn lessons from the past, learn about life. Sometimes it can be the result of a trauma or depression, too.
"I've already spent a lot of time hermitting about you. Had a lot to learn from this poking and questioning, but I think I covered most of the You question now."
For example, when you get dumped by a loved one, you'll often question yourself for a long time about what happened that caused the failure. Sometimes when you really want answers, you'll tend to avoid noise and people. This is what I call "hermitting". This behaviour can get compared to that of a hermit, because the person rather spend time alone, to think, than with people having fun and socializing.
Sometimes, after a major turn in life, hermitting can be a necessary phase of "digestion of events" before being able to move on.