Before the age of four or five, most children have little concept of money and its function. Older preschoolers begin to understand its usefulness—and may want some of their own.
Giving your four-year-old a small weekly allowance can provide a helpful introduction to the idea of money management. Your preschooler does not need a lot of money, but that's not really the point.
If he has his own money, your child will begin to appreciate how much the things he wants cost. He will begin to make decisions as a consumer—whether to buy a candy bar or a coloring book. And if he wants something really badly, your child may even begin to save his money in anticipation of the future.
If you do decide to give your preschooler an allowance, try not to link it to doing his chores or helping around the house. Allowance, especially for preschoolers, is pocket money—nice to have but totally unnecessary. An allowance is not a payment for doing his chores. He should be encouraged and expected to help around the house not because he gets paid for it, but because he's a contributing member of the family.