to embarrass oneself in front of a decently large audience, usually done in a public place. The action is symbolized by the image of defecating in a pool because in such an event, everyone knows who "shit the pool", causing that individual major embarrassment.
Charlie: "I had the worst day ever. my pants fell down in the middle of my presentation."
Bob: "It's ok, man. Sometimes, you just gotta shit the pool"