Improvements made to Pets, giving them careers, being able to teach new tricks, and more!
To learn more about the Main features of Life Improvements take a look at LI General, for information about modules for LI, take a look at the various Module pages.
Same way you get a Human Sim promoted, except the criteria for promotion reqires teaching the Pet tricks relevant for their Job. Such as Fetch for a Security Animal or Sit for a Service Animal.
Horses require gaining certain skills such as Agility for Show Biz or Temperament for Service, check their career panel for more information.