In blockchain terminology, a mempool is a waiting area for the transactions that haven't been added to a block and are still unconfirmed. This is how a Blockchain node deals with transactions that have not yet been included in a block.
Front-running is the “act of getting a transaction first in line in the execution queue, right before a known future transaction occurs.”
A mempool bot is a bot able to scan this waiting area, so as to be able to buy a token as soon as liquidity is added --> in the same block
A front-run bot is a mempool bot, but configure to "sandwich" your transaction. When it detects your transaction in the mempool :
It buys a lot of tokens right before you, to make the price rise
YOU buy at a very high price
It sells this tokens he just bought, and make benefits