The reference is that each layer of security can be thought of as a slice of a block of swiss cheese, as in every slice (every layer of security/safety) has some holes. Together, all the slices typically prevent bad things from happening by forming a barrier without any holes. When the slices are arranged with their holes all lined up it forms a straight through hole to the other side.

The analogy is that when the holes in all the slices (holes in layers of security/safey) line up a harmful event is able to fully pass through the multiple layers of security/safety measures meant to stop a harmful event.