It works like this:
You visit the site and register a promise, let's say, to paint a house. A few days later you meet someone who has something you want: a puppy for sale. You offer to pay with the promise. The puppy owner takes the deal, maybe because he has 5 puppies and he might not have sold the last one anyway. You inform the site of the change of ownership. The following week the dog owner is at a dog food store. He offers to pay for a months supply of dog food with your house painting promise. It sounds like a good deal to the dog food store owner who got the food wholesale. Again the site is informed and updates the owner registry.
And so forth. Your promise has become money. It might never be owned by someone who wanted to call in the promise and have the painting done.
If that happens, you as the promise maker can pay someone else to do the job, maybe by exchanging another promise you own to pay. Or you can do the job yourself as you promised!
If you don't perform this will be recorded on the The Promise Bank site. Your reputation will suffer. That mean your future promises might be valueless.
Artists are commissioned through The Promise Bank to make paper certificates for different types of promises, to be signed and numbered, and sold to promise makers as collectors items and of course to be traded too. The site is still informed of ownership as security against counterfeiting.