A Boolean object combines two or more objects by performing a logical operation on their geometry. The objects typically overlap, but they don't have to. The original two objects are the operands and the Boolean object itself is the result of the operation.
The following illustration shows some typical Boolean operations:
The fence is operand A, and the cat is operand B.
Upper left and right: A minus B
Second to upper left: B minus A
Second to lower left: Union
Lower left: Intersection
For geometry, the standard Boolean operations are:
In addition, Boolean operations are available with editable splines and Body Objects.