Naked and bare are both adjectives; bare can also be a verb. Jay compared naked as an adjective with bare as a verb, which is a bit confusing.
Naked is usually used to describe an unclothed person, and it usually means 'completely without clothes'. Bare can be used to mean the same thing, but is more generally used to describe a partial lack of clothing - I currently have bare arms and legs. I am also bareheaded, i.e. I am not wearing a hat.
As an adjective, bare is also often used to describe other things: a bare mountain has no trees; a bare living is a life with no luxuries; in computing, a bare metal server has no operating system.