Refers to the mythical tengu creature or metaphorically to a conceited person; 増長天狗 is a more specific and rare compound emphasizing boastfulness.
A more common word for a braggart or boaster, without the mythological connotation.
Compound of 増長 (ぞうちょう, 'growing conceited') and 天狗 (てんぐ, 'tengu'), a mythical creature often depicted as arrogant and boastful. The exact historical derivation is uncertain, but the word figuratively describes a person whose conceit has grown to resemble that of a tengu.