The way I understand it's just a way to outsource the generation of your vanity addresses, essentially you will in the end get the pair of private and public keys while not exposing the private key to those who helped you in generating it
You will be generating a half of the private and public key. You will then be sending your part of the public key.
They will use your part of public key to combine with their part of public key to form addresses. When they find the desired sequence when combining your public key and their public key, they will send you their part private key. Combining their part private key and your part private key will generate an address that corresponds to the desired address. It's called split-key generation.
They cannot spend anything without your part private key.