Starting in my early teens, my parents gave me a weekly allowance. I believe the purpose was for me to be able to buy certain wants that weren't considered essential, instead of me having to ask them each time for money to buy a soft drink, candy bar, etc. Having an allowance gives a child a certain dignity and lesson in managing small amounts of money.
Allowance or no allowance, I was expected to do chores, such as mowing the yard, helping clean the house, and starting supper when I got in from school. If I had refused to do chores, they may have suspended my allowance - I don't know - that never became an issue for us.