How do you accelerate transactions? What doesn't that mean? Adding additional miner fee after it's been sent?
It's a fancy name that implies that your transaction be confirmed quicker. It doesn't actually do anything to the transaction itself or the network itself.
These acceleration service providers, such as the one cissrawk used to submit your tx are actual miners. When they accept your tx, they just promise to include it into the next block they find. If they find a block and the network accepts it, it's added to the blockchain and your tx, which was included, is confirmed.
So, your tx confirmation has an improved chance of getting confirmed: either still being picked up by other miners or when the accelerating miner finds a block.
The other individuals in this forum also providing the service either are miners themselves or are able to ask miners to include txs.