Definition of talk up phrasal verb from the Oxford Advanced Learner's Dictionary to describe somebody/something/yourself in a way that makes them/it/you sound better than they really are They talked up the tourist attractions to encourage more visitors.

talk up (third-person singular simple present talks up, present participle talking up, simple past and past participle talked up) (idiomatic, transitive) To talk about (something or someone) to make it seem as good as possible or to draw positive attention to it.