The word has a couple of meanings depending on the context in which it is used:
1. The word is used to refer to a pay phone.
“When i grew up we used to use a tickey box to call home.”
2. It is a word used to refer to blank squares on a box that need to be ticked in order to indicate your selection.
“I see that they have added other under the gender tickey boxes.”
Alternative spelling: ticky box