Originally Posted by
Crake
It's a magical pact that they agree to, being bound to their world (hence the planar binding). The planar binding spell facilitates the ability to make the pact, but it is ultimately up to the bound creature to agree. The charisma check is a mix of you forcing your will on the creature, but also how enticing you're able to be, but it is ultimately up to the DM to determine if a bargain is something the creature would consider unreasonable, so the DM always retains veto power to say no to your pact regardless of what you get on your opposed charisma check, but may also do the opposite, where if your request is reasonable enough, he would simply allow the creature to agree without the need to roll a dice.