What does transactions accelerators for BTC?
Transaction accelerators are services offered by people who have direct access to a mining pool (and to the list of transactions going to be included).
One a transaction is 'submitted' for acceleration (either free or paid) the miner most likely will include this specific TX into the next block he is going to mine.
Those were helpful when fees were significantly higher and a lot of people chose a fee which was too low. This has led to a massive amount of transactions waiting to get confirmed.