There is limited space on the block, so not all transactions (tx) waiting in the mempool can be placed into the block. Accelerators are simply a commitment by the corresponding pool to include the requested tx over all other tx in the next block they find.
So I am guessing they would pay more? And is there more than one mempool? Some yes. Some offer it for free but with a limited quota per hour.
There is one mempool per node in the network. They should be similar, but not always identical.
Each transactions also has a slot for optional fees to be collected by the one constructing the block. So transactions in the mempool tend to be added to blocks in a predictable way. Most recent wallets come with a fee estimator to position the transaction in a favoriable place.
The accelerators is like a fast pass for future blocks found by the pool offering the service.
You can check number of transactions in the mempool e.g. here:
https://blockchain.info/en/charts/mempool-size?timespan=60days
