Self-praise couched in self-deprecation, in modern lingo

• "Man, I'm gonna be sore for a week after bench-pressing 350 pounds," e.g
• Show false modesty
• "I'm kind of embarrassed how many people mistake me for George Clooney and ask for my autograph," e.g
• Claim that your biggest weakness is being a perfectionist, e.g

Wiktionary Word definitions in Wiktionary
n. An ostensibly self-deprecating statement made to show off. vb. To make a humblebrag.