There are lots of reasons.
A movie theater rents the movies it shows. In order to maximize revenue, and profits, the theater might charge less in the afternoon, when there are normally less patrons. Perhaps they would like to see more adults in the theater (adults have more money to spend on food and drinks which are profit producers) so they charge a lower fee.
Airlines have to bring their planes back to their home, so they might charge reduced fares on return trips to try to fill the plane. They might offer discounts for advance purchases, because then they can plan their business better. Airlines might reduce fees for frequent fliers, hoping to get repeat business. Or they might hope that the frequent flier will upgrade to business class, etc...
Some businesses might raise costs -- if demand is too high at a particular time then they charge more.
Older customers tend to be more "brand" loyal, so giving seniors discounts, etc... might help with continued business.