Hi! Ancient knowledge instants provide a certain (1, 3, 5,15, 20, etc) amount of KPs to any Ancient Wonder you wish.
Ancient Wonders are special buildings that you unlock in your tech tree - I believe starting somewhere around chapter 2 or 3. There are many different kinds, as you progress through the chapters you accumulate the ability to build them all. Once built, they require a certain amount of KPs to upgrade. And so...the Ancient knowledge instants can be used in addition to the regulal KP you acquire each hour of the game.
Ancient Wonders and the instants that go with them have a wide range of uses and benefits which I won't go too deep into but you can follow this link to a
helpful site that will tell you all about them!