They varied greatly depending on their members. This ranged from exclusive aristocratic institutions to profession or trade based (the Oriental Club), politically-affiliated (National Liberal Club), interest based (the Arts club) etc. There was more or less a club for any "gentleman" who cared to belong to one. Some would have a strict process of nomination and election for members (see the idea of being blackballed, where a member putting a blackball instead of a white into the box barred a nominated person from entry). What club you belonged to and could get entry to could be a delicate matter of social status.

And their character varied depending on the membership, some were notorious for gambling (White's for example, where Lord Alvanley infamously bet £3,000 on which raindrop would reach the bottom of a window first).

Generally they were for social gathering of like-minded (and often like-classed) men, some offered lodging for members (if they say needed to be in London but either didn't own property there, or didn't wish the hassle of opening up a house that'd been shut up), most offered food and drink, usually a library. They could be a convenient place to entertain visitors, meet friends, avoid your wife, etc.