1. Literally, to contract one's muscles, especially to demonstrate their size and strength. He's so vain, flexing his muscles in the mirror whenever he thinks no one is looking. She flexed her muscles and told us not to mess with her brother again.

2. By extension, to demonstrate one's influence, power, or strength. The small but outspoken nation has been flexing its muscles lately, with a wide range of military demonstrations. The wealthy business tycoon flexed his muscle to get the charges dropped against his son.