Boast about your own achievements. Draw attention to yourself. Usually, the easiest way to do that is to make a lot of noise. Although I suspect that if you really want to catch someone’s attention, whispering might be a better choice.
Phrases meaning the same thing have been in use for centuries. For example:
Beat your own drum.
Toot your own horn.
Scream your own song.
Pat oneself on the back.
Give oneself a round of applause
The term in its present form is from the 19th century. The first printed example we know of is in Anthony Trollope’s work Australia and new Zealand, 1873.
The King James Version of the Bible, 1611 also includes a warning against boastfully ‘blowing one’s own trumpet,’ although not in those precise words:
6:2 Therefore when thou doest thine alms, do not sound a trumpet before thee, as the hypocrites do in the synagogues and in the streets, that they may have glory of men. Verily I say unto you, They have their reward.
6:3 But when thou doest alms, let not thy left hand know what thy right hand doeth:
It has also been suggested that the phrase may refer to the practice of heraldry. It comes from the sense of ‘horn’ as a trumpet, and one who blows his own horn is someone making great fanfare about himself, as is usually more appropriately left to a herald.
Important men used to have heralds to announce their greatness. Modern newly married couples use automobile horns to announce their status. When I want to make a noise about what I’m doing, I post to FaceBook, a much quieter way of blowing a horn.