Use the following options to set what happens when you select Surfaces > Booleans > Union Tool/Difference Tool/Intersection Tool.
Maya can keep a construction history input from the original surfaces so you can transform them to change the resulting boolean surface. If you do not want to keep this history input, turn on Delete Inputs. Also, construction history must be turned off in the scene. If construction history is on, Maya keeps the history inputs, regardless of this option.
Exit On Completion, when turned on, takes you out of the Boolean tool after the Boolean operation is calculated. If turned off, the boolean tool remains the current tool so you can continue to perform other Boolean operations.
The Hierarchy Selection option ensures that you can successfully perform a Boolean on the result from a prior Boolean operation. When on, Maya selects and performs the Boolean operation on the root of any given hierarchy. You must turn off Hierarchy Selection if you want to perform a Boolean operation on objects that are within the same group.