This is arbitrary, and the pool chooses what they are confident with.
Some number of confirmations are needed to ensure the pool really has the mined monero before they pay miners. If a pool were to pay miners as soon as it mines a block, it would risk that block being orphaned (ie, another block takes its place on the chain), and it would have paid money that it does not, in fact, have, causing monetary loss to the pool. Since it becomes harder and harder to orphan a block as it gains confirmations, waiting fixes that problem.
Another reason for most pools to wait for 60 confirmations is that coinbase tx outputs are locked for 60 blocks, so those new monero are unusable for 60 blocks after mining. If a pool wishes to pay miners before 60 blocks, that pool has to have enough other monero to cover those young blocks.