They are opposites of one another. They are often used in terms of money.
To Borrow: To take something, and later return it. Casually, this is very often used as "can I borrow [item]?".
To Lend: To give something, and later receive it.
Ex. "Hey John, can I borrow five bucks?"
Ex. "I lent Oscar five dollars, but he hasn't paid me back for a week!"
Ex. "I went to the bank to borrow money for a car."
Ex. "Hey, can I borrow an apple?" (The person borrowing probably does not intend to return the apple in this case.)
Ex. "Neither a borrower nor a lender be = Do not lend or borrow money" (from Shakespeare's Hamlet)