"吹牛 ( chuī niú)" means to talk big but ignore the facts. In order to make him/her important, the speaker usually tells others his/her made-up high social status, strong points and abilities. We can also describe this behavior as "吹牛皮" (chuī niú pí)."吹牛 (chuī niú)" can also be used independently as a response to other's statement, which suggests the speaker does not believe what the other said, and think he/she was just bragging.
1. Tā zǒngshì ài chuīniú, dōu méirén xiāngxìn tā le.
He is always talking big, so no one trusts him anymore.
2. Tā chuīniú shuō tā zhècì kǎoshì kěndìng néng kǎo mǎnfēn.
He brags that he will get full marks in this exam.