What do we do with the intriguing stone in X/Y ?

Question

I have it in my key items pocket and I do not know what to do.

Answer 1

Intriguing is a Key Item that was given to you by Tierno in order to aid in the research of Mega Evolution and it has no added function.
What should you do? Give it to a hiker near the stairs in Cormarine City and you'll get a Sun Stone in return.
This video can help you.

Hope this helps.

Answer 2

Exchange it with a Hiker in Shalour City for a Sun Stone.

Source.