The word "scene" has many meanings. One of the meanings is "a certain field of activity." For example, if a person is involved in politics, he might say "Politics is my scene." (= Politics is what I'm involved in.) Or if a person loves the theater, he might say, "I love the theater. It is my scene." ( = The theater is what I am involved in.)

Hi Gordon, I think Neil's answer below is very good but you should also know that this is probably not an expression people of your age would use. It is a bit outdated. Hope this helps.