The shorter more practical explanation is kids do the thing they will be rewarded for and earn tokens (points, chips, tickets, etc) that they can exchange for something they want.
A token economy is a system where something, a token, represents a unit of value that can be exchanged for an item or service equal to the value of tokens exchanged. Really if you think about it, it’s basically any non bartering economy as pieces of paper and coins are simply the tokens we use.
Token economies are based on principals of operant conditioning and the work of BF Skinner. Skinner studied and wrote about behavior modification through the use of consequences and reinforcement.
He and others also showed how to best use reinforcement by trying the different possibilities of reward structure. For example, giving the same reward every time or varying it and giving the reward every time the behavior is performed or randomly.