The person who needs money and asks another person for money is the borrower, so he borrows money.
The person who has money and is happy to give it to the other person for a short period of time is the lender, so he lends money.
Remember this sentence: I need to borrow some money.
It is unlikely that a person who already has money will feel it is necessary to give that money to someone else for a short period of time. However, "I need..." shows that the person lacks something (in this case, money) and therefore needs to "borrow" it from someone else.