Predicate methods in Ruby are special methods that end with a question mark. They always return true or false based on a condition. For example, the method even?(num) checks if a number is even by using the condition num % 2 == 0. When called with 4, it returns true, and with 5, it returns false. These methods help make code easier to read by clearly showing they answer yes/no questions. The execution table shows each step: calling the method, evaluating the condition, returning true or false, and printing the result.