Sister companies are two or more companies owned by the same (parent) company.
Assume that Pepsi buys Taco Bell and Pizza Hut. Pepsi is the parent and Taco Bell and Pizza Hut are the kids. Like many other things, we use the femine form and call them sister companies (rather than brother companies). The use of parent and sister terms comes from the common reference to groups of companies are a family of companies.