1. express gratitude or praise
big up to my mentor/teacher
To 'big up' someone or something is to praise or rate the person or the thing in an enthusiastic way that draws attention or publicity. This is often used in relation to celebrities promoting each other and each others' work. It can also be used in professional contexts: "Graham has really bigged you up. I'm very excited to hear more about what you can do for us." This is used more in casual conversation than in formal settings. Add a hyphen and you make 'big up' (phrasal verb) into a noun (a big-up): "I'd like to give a big-up to all my friends out there. Thanks for supporting me."