Essesntially Bitcoin transactions are grouped together and put into a block, this block then will be processed by the miners, hence the term mining. Every transactions in that block will receive confirmation from the network and then the process repeats.
What transaction accelerators do is basically asking for the miners to put that particular transcation to be prioritized and be put in the next block.
For example, you can ask viabtc to put your transaction into their priority list, although it's only limited to 100tx/hour
https://viabtc.com/tools/txaccelerator/Never fall for paid accelerators on this forum as most of them are a blatant scam by using free accelerator to push your TX
Heck, some of them didn't even do anything on your transaction and just hoping for a luck that your transaction will be put in the next block