When you're a kid, you might earn an allowance or a sum of money in exchange for doing chores around the house. Your parents' allowance — or tolerance — of your silly behavior will depend on how strict they are.
An allowance is a quantity of something that's allowed or permitted within a set of rules or for a particular purpose. This could be a weekly allowance you earn as a kid, or it could be the allowance for passengers on a flight to have two carry-on items. To make allowances for someone means to treat someone leniently, or to give them a break.