If you 'run something by someone' or 'run something past' someone, it means to approach someone in order to get their opinion on something or their approval. You will often hear this expression in the workplace but you can use it in social contexts too.

1. Sorry, I didn't quite understand what you were trying to say. Do you mind running it past me again?
2. I'll have to run it by my housemates, but I am planning to have a party at my house for my birthday.

1. Before we sign anything, I just want to run these documents by our legal team to make sure everything is above board.
2. In my meeting with the boss, I ran a few ideas past him about ways we could improve our efficiency. He was very receptive.