They see red, green, blue, and then I'm guessing about 12 different variations of polarized light. Which they use in coloring their tails to communicate with other mantis shrimp, because only the other mantis shrimp can see the patterns in the tail, and receive the message.
Imagine there's all these people around you, and your paramour has these plates on their forehead. And only you can see them. Your lover can send you messages and nobody else, not even the NSA, can see that the messages are even there, let alone decipher them.