Semantics of "on" versus "in"

When talking about locations: "on" means being located on top of a certain surface, and "in" inside another object: Compare on the box and in the box. This is the major difference in their meaning.

They are also used to denote a number of other relationships, such as "in December", "on Friday" but I would say that their usage there is more metaphical and idiomatic: and the major semantic difference is between "inside" and "on top of".