If you happen to be sophisticated, it means you have a good knowledge of art, fashion, politics, etc. It also implies having a lot of knowledge and experience of difficult or complicated subjects and therefore being able to understand them well.
In American literature masterpiece "Great Gatsby" by Fitzgerald, one of the main characters - Daisy - says the famous sentence: "Sophisticated! God, I'm so sophisticated!"
Definition: having experience, knowledge of art, fashion, etc
Example: I've travelled the whole world. I'm so sophisticated!