What to Do if Your Bitcoin Transaction Gets "Stuck"
The number of transactions on the Bitcoin network has steadily increased over the years. This means more blocks are filling up. And as not all transactions can be included in the blockchain straight away, backlogs form in miners’ “mempools” (a sort of “transaction queue.”)
Miners typically pick the transactions that pay the most fees and include these in their blocks first. Transactions that include lower fees are “outbid” on the so called “fee market,” and remain in miners’ mempools until a new block is found. If the transaction is outbid again, it has to wait until the next block.
This can lead to a suboptimal user experience. Transactions with too low a fee can take hours or even days to confirm, and sometimes never confirm at all.
A mining pool may offer a premium service in which they will prioritize a transaction, usually for a fee. The ability for that pool to get a transaction confirmed is limited to their ability to get a block confirmed -- and most pools have a tiny fraction of the hashrate. For example, if a pool has 10% of the hashrate, they mine about a block every 100 minutes (1 hour and 40 minutes), on average. If a pool has 5% of the hashrate, then they mine one block about every 200 minutes (3 hours and 20 minutes), on average.
There are additional services claiming to be able to "accelerate" a transaction. Their ability to get a transaction confirmed faster is limited to re-broadcasting your transaction, to help in the situation where that mining pool has dropped your transaction already. The Bitcoin Core client already does re-broadcast a "stuck" transaction periodically to peer nodes, though these services possibly may broadcast a transaction directly to known mining pool nodes. These services could also pay a mining pool to include your transaction, just as you could do that yourself.
It is likely these "transaction accelerators" that are not the mining pools themselves are not actually helping to get a transaction confirmed faster.
The recommended approach to "accelerating" a transaction is to perform a fee bumping method which is available to either the sender and/or the recipient of a Bitcoin transaction.