To give up means to stop trying to do something or to stop believing you can succeed at it. When you give up on a difficult math problem, you put down your pencil and walk away instead of trying different approaches. When a runner gives up during a race, they stop running even though they could keep going.

Giving up is different from making a smart decision to change course. If you're trying to break through a brick wall with your bare hands, stopping isn't giving up, it's being sensible. But if you quit practicing piano after one frustrating week because a song feels too hard, that's giving up, because you know that with more practice you could learn it.

The phrase often carries a sense of surrender or defeat. In sports, a team that's losing badly might give up and stop playing with full effort. A detective might give up on solving a cold case after running out of leads.

People also use “give up” to mean surrendering something willingly. A seat on the bus can be given up to someone who needs it more. A knight might give up his sword when defeated in battle. During Lent, some people give up chocolate or video games as a form of self-discipline.