Literally 'to blow up an ox.' Origin story: Yellow River raft-makers had to inflate ox-hide rafts by blowing into them - an impossible-sounding feat, hence 'blowing an ox' = talking nonsense.
The full version is 吹牛皮 ('blow up an ox hide'). On the Yellow River, people made rafts from inflated animal skins. Blowing up a whole ox hide by mouth was considered impossible - so someone claiming they could was obviously a braggart.
usage
Very colloquial and common in daily speech. 别吹牛了 (Don't brag!) is something you'll hear constantly. The related noun 牛皮 can mean 'bragging' in slang: 吹牛皮 = 吹牛.
