I think that when the developers started implementing RBF, they used a very misleading word as a verb to this procedure. Double spending is prevented using a peer-to-peer network as the whitepaper says, but they chose that phrase as the proper one for RBF. Maybe a better formulation would be re-broadcasting or broadplacing?
Double spending is impossible in Bitcoin if and only if you're looking at the blockchain alone; a single chain cannot have two of the same inputs being spent twice. You can however, choose to spend an input that has been spent before and is currently in the mempool. Technically, by being able to broadcast a transaction which spends the same inputs as another in the mempool is regarded as double spending it, though obviously the other gets kicked out.
This is not an accelerator as some of the users here are claiming. This is a site to broadcast two competing transactions by broadcasting a conflicting transaction after the other. This site isn't intended to help users to use RBF to unstuck your transaction but rather to help users intentionally replace a current transaction with their own. You can do so with any wallet that support RBF.