Meaning
Stand tall and be proud — literally 'puff up your chest'. It is an encouragement to hold your head high, take pride in yourself or your achievement, and carry yourself with confidence and self-respect. To 'big up yuh chest' is to square your shoulders and show that you are somebody, refusing to shrink or feel small, and it is offered as a boost to someone who has done well or who needs heart to face the world with their dignity plainly on show.
Examples
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Yuh done good, so big up yuh chest.
You did well, so stand tall and be proud.
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Nuh mek dem put yuh down — big up yuh chest.
Don't let them put you down — hold your head high.
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Wi win di ting; big up yuh chest, mi bredda.
We won it; be proud of yourself, my brother.
Origin
A body-language image: pushing out the chest is the posture of pride and confidence — 'big up' (to boost or exalt) applied to it means to carry yourself proudly.
How it’s used
An affirming expression of pride and encouragement. Related to the wider Jamaican use of 'big up' (to praise or salute someone).