why do geckos make a clicking sound?

Answer 1

Because they can. ;)

Noices for reptiles depend a lot on when they make them. It clicks when you pick it up or hold it, it's a fear/stress sound.

It clicks in the middle of the night when you're asleep or there's really nothing going on, it's most likely calling for a mate (Not that it -needs- one, mind you.).

Just be glad you don't have a Tokay gecko, they don't click, they yell, "GEC-KO" or, depending on who you ask, "TO-KAY" loud enough to wake you up at night.

Answer 2

I have Leopard Geckos, and when they make a clicking noise, it is usually to warn you they don't like something.