big up

(Jamaica, slang, idiomatic) To proclaim or exaggerate the importance of.

Example:   He works out every day to big up himself.
  I want to big up my bro on the mic.
  They're trying to big themselves up to be more than they are.
2007 In a keynote speech, attended by over 2,000 people, Steve Jobs spent the first 10 minutes bigging up the move to Intel chips. — Apple announces new mobile phone, BBC Online, 9 January 2007