Your account number is the only thing a company needs to switch you to an alternate energy provider. All you need to do is show them a copy of your bill (or tell them the number over the phone) and they will switch you against your will. At that point your supply charges (which pays for poles and power lines into your house) still goes to PSE&G but rather than choose the cheapest available power generator, you now buy your power from whatever company you switch to.

People sometimes do this because they want their power bill to go toward some kind of environmentally friendly company but rarely will switching ever save you money. If someone cold calls or approaches you, it's a scam.