1. Keith lets everyone know that the boss is going to make him the new assistant manager. He likes to blow his own horn.
2. Ruth won’t make many friends if she keeps blowing her own horn about her accomplishments.

Dating back to at least the 16th century, this phrase is a reference to the practice of blowing horns to announce the arrival of important officials such as kings. To blow one’s own horn is to boast or claim a position of superiority over others.