To be inventive is to be creative. Inventive people are good at using their imaginations.
If you know that inventors create new things, then it makes sense that the word inventive applies to people and behavior that show creativity. Artists are inventive, especially if their work is different than other people's work. Little kids are very inventive: their imaginations have almost no limits. People who copy others aren't inventive, because they're not being original. When people are being inventive, new ideas are flowing.