The point system is the one where the customer gets some points for every money they spend. For example, each dollar spent makes customer earn one point, or in the case of airlines each mile travelled gets one point or each night spent at the hotel gets some points etc.
Along with regular points, business can also release reward offers like receive double points for flying direct in August or collect double points for buying any promotional products.
Customer collect points for a certain period and business will release redeem offers regularly where customers can spend their points to get a product or service at a discounted rate or for free.
Point system is generally run by big corporates where they have many products for sale like groceries store or big price item for sale like air ticket. They analyse the points collected over a period of time and come up with a reward or redeem offer to best suit their business needs. For example- a clothing brand is going out of fashion so they can give a double point offer or give a discount price offer if the customer has some point already collected. Similarly, airlines or hotels can give a discounted price for customers to increase their bookings.