What it means
Benching is keeping someone you're dating on the sidelines as a maybe, not breaking it off but not really moving forward either. You send just enough texts to keep them interested while you weigh up better options, like a manager leaving a player on the bench in case they're needed. It strings someone along without ever picking them.
Usage examples
"I think he's benching me, he texts once a week and never actually asks me out."
"Stop benching her, either commit or let her find someone who actually shows up."
"She's been benching him for months, popping up with a hey stranger whenever her main thing goes dead."
"Nah, don't answer that at 1 a.m., she's not serious, she's just keeping you on the bench."
Where it comes from
It comes straight from sports language, especially team games where a player gets benched and left waiting instead of being put in. Dating slang lifted that image in the 2010s to describe someone being kept around as a backup option, not chosen, not fully dropped either.