According to the youtube video, Alice pays Bob $0\mathrm{.}42$ BTC and leaves $0\mathrm{.}001$ BTC to the miner. The reason for this $0\mathrm{.}001$ BTC to the miner is:

to give the miner more incentive to include her transaction in the block

to lower the target hash value so that the miner can use less advanced computer chips to solve the puzzle

to create a new network in the blockchain for the transactions with transaction fees

to expedite the mining process so that the new block will be created in less than $10$ minutes