Można is impersonal and means 'can I?' or 'may I?'
Not exactly. It can be used in such contexts, but for better understanding it'd translate it like: Is it allowed? or Is it possible? or Is it doable? It may also be used to answer there questions like:
(Czy) Można? (Tak,) można. Is it allowed? Yes, it is.
Gramatically, it is so called 'predykatyw' (not sure if it can be translated as 'predivative', because Wikipedia defines it a bit differently).
These words work in sentences as verbs, but are not verbs (i.e. they do not conjugate), and are used to describe some 'general state', not someone actions.
There are quite a few in Polish. e.g. można, trzeba, wiadomo, widać, słychać. They form tenses by using an auxiliary verb 'być' in the appropriate tense. E.g.:
Present Można - it is allowed to...
Past Można było (or było można) = it was allowed to...
Future Można będzie (or będzie można) = it will be allowed to...
They are a little similar in their function to adverbs, and historically they probably were adverbs.