The Hollywood principle is the design principle that is summarized by Don't call us, we'll call you. It comes from the Hollywood philosophy where the production houses call actors if there is any role for the actor.
In the object-oriented world, we allow low-level components to hook themselves into the system with the Hollywood principle. However, the high-level components determine how the low-level systems are needed and when they are needed. In other words, high-level components treat low-level components as Don't call us, we'll call you.
This relates to the Template Method pattern in the sense that it's the high-level abstract class that arranges the steps to define the algorithm. Based on how the algorithm is, low-level classes are called on to define the concrete implementation for the steps.