To let is to allow or permit. If you don't prevent your little brother from jumping off the roof into a pile of leaves, you let him do it.
Your boss might let you take a few days off work, and the friendly city bus driver might let you ride for free when you forget your wallet. Another way to let is to allow someone or something to pass in a certain direction, like a window that lets in the morning sunshine. The word can also mean "lease" or "rent," so a landlord might let a room over his garage to a college student.