Does "вчити" means "to teach" or "to learn"?

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Both) Depending on the context, the word «вчити» can mean both «giving knowledge to someone» (to teach) and «learning something» (to learn)

To explicitly refer to one of the meanings there are following words:
to learn: засвоювати, опановувати, вивчати (last one is exactly «to learn»)
to teach: навчати (exactly «to teach»), повчати (rather when a wiser person gives advice to not so smart person)

(In all the examples, keep in mind that the sentence can be translated in both Present Simple and Present Conituous)
я вчу історію (I'm learning history / I learn history. )
я вчу дітей (I teach children)
діти вчаться у мене (I teach children)
діти вчать мене (children teach me)
ми вчимося (we learn)
ми вчимо (we teach)