If the name of a modifier is higlighted in red, it means that the Modifier is currently not having any effect because its parameters don't produce any effect (for instance, if you add a Subdivision Surface with level "0").
In your case, your Boolean modifier hasn't got an effect because you haven't selected an Object in the "Object:" dropdown menu of the modifier.
Indeed, the boolean modifier doesn't work by selecting two object and adding a modifier, but selecting ONE object, adding the modifier, and telling the modifier what other object to use for the operation
Example usage of Boolean: cutting part of the green cube using the white cube
Note that only the green cube is selected. The white cube is just chosen for the operation. As soon as the choice is done, the red highlight under "Boolean" is gone.