Describes a person's boastful or swaggering attitude; often used with する to mean 'to brag' or 'to show off'.
He always talks about his success in a bragging way.
Please stop showing off.
威張る is the verb 'to be arrogant' or 'to act big'; 大威張り is the noun/adjectival noun form with an intensifying 大.
Standard kanji spelling.
Mixed kanji-kana spelling; common in casual writing.
Compound of 大 (おお, 'big') + 威張り (いばり, 'boasting'), the noun form of 威張る (いばる, 'to be arrogant'). The exact historical derivation is uncertain, but the word likely emerged as an emphatic expression for boastful behavior.