Eidos is an ancient philosophical term; loosely speaking, it means the information that makes up an object we then perceive through the material world. When we see something – for example a chair – we see the manifestations of it’s properties – we see wood, four legs, we can even estimate weight, height, velocity, and thousands of other conceptual variables we cannot see. Eidos is where all those variables are defined. The material manifestation directly effects Eidos – if you kick a chair, you suddenly add directional acceleration to it, and you may even – depending on it’s properties of durability – break it into different objects.
The opposite – the altering of somethings properties in Eidos effecting the material form – as it turns out, is also true. This is what we call Magic.
The Eidos key is a theoretical concept by people that study how magic works, and is the so called "missing step" between been calculation and actualization. To use magic, a mage must first conceptualize the change, then calculate it, and then actualize it into the world. Many researchers delve into how a mage takes a calculation applies it to the world, but many leading theorists support the idea of a so called "Eidos Key" unique to humans that allows them to interface directly with Eidos.
Several attempts have been made to make an artificial Eidos Key to make a computer fully capable of independently activating magic, but so far no one seems to have succeeded. Well, unless you count I.L.A., but that is a little controversial currently.