When you paint a picture of someone, either in words or in paint, you portray them. Actors portray characters too.
Whether you're talking about acting or another art form, the idea is the same: representing a person and bringing to light their most important qualities. To portray a person is to show who that person is, giving a sense of their personality or character. Often, famous people don't like how they're portrayed. For example, Presidents usually hate how they're portrayed in editorial cartoons. When you portray someone, you can be positive or negative, accurate or inaccurate. It's up to you.