Meaning
To praise, celebrate, and publicly give respect to someone — to hail and honour them. It works as a verb ('big up di whole crew') and as a standalone salute thrown out to acknowledge a person's presence, achievement, or support ('big up yuhself!'). A cornerstone of dancehall and everyday courtesy, to big someone up is to lift their name and give them their due out loud, and the giving and receiving of 'big-ups' is a constant, warm ritual of respect.
Examples
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Big up yuhself, mi bredren!
Respect to you, my friend!
The most common form — a direct salute.
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Mi waan big up di whole a mi family.
I want to give respect to my whole family.
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Di selecta big up di crowd before him drop di tune.
The DJ saluted the crowd before playing the song.
Standard dancehall and sound-system usage.
Origin
Built from English "big" used as a verb with the intensifying particle "up", a productive pattern in Patois (compare "mash up", "buss up"). Spread internationally through dancehall and sound-system culture from the 1980s onward.
How it’s used
Warm and public by nature — it is an acknowledgement meant to be heard by others. Now common in British and North American slang, often without the original sense of showing respect.