To my knowledge, it's used to describe someone who tries too hard to be unlike other people. Like all of the cringey videos of younger people saying, "I'm not like other girls."
Being overly adamant that you don't fall within societal norms screams "pick me" energy and just makes it seem like you're as basic as anyone else.
It's also generally used towards women. "Pick me" girls focus on highlighting their less effeminate traits or things that they think men will find more attractive in order to be "picked" instead of just being themselves.
I've also seen guys use it towards other guys. Like when a man makes a comment defending a woman when other men are attacking her. They call him a "pick me."
It's a weird phrase and I've never actually met someone in real life who I'd refer to as a "pick me." Not that I'd refer to someone as that online either. Seems more like something others use as an insult when they think someone is being "fake" on social media.