To allow means to give permission for something to happen or to let something be possible. When your teacher allows you to work with a partner on an assignment, she's saying yes, you have permission. When a theater allows food inside, they're permitting people to bring snacks.

The word carries a sense of power or control: someone or something must be in a position to say yes or no. Your parents might allow you to stay up late on weekends. A basketball referee allows play to continue or stops it with a whistle. City laws allow buildings to be only so tall.

Allow can also mean making something possible without involving permission. A wide doorway allows furniture to pass through easily. Good weather allows an outdoor concert to happen. Your savings might allow you to buy that book you've wanted.

Notice that allow is slightly more formal than let. You might say “Mom let me go to Jake's house” in conversation, but “The rules allow students to use the library during lunch” in writing. Both words mean essentially the same thing, but allow sounds more official or proper. When you allow yourself to try something challenging, you're giving yourself permission to take that risk.