Preface: I am not an expert. Smilies to increase Goomba-Friendliness Index (GFI).

Anyway... First, as far as I understand it Exposure Index (EI) in the true use of the term is only relevant when discussing real film photography. In such cases it pretty much means a temporary working ISO for a piece of film stock. An example from the good ol' days of film might go like this...

You find yourself in need of shooting some fast moving subjects outdoors in the dimming light of evening. Looking in your camera bag, all you have is some ISO 200 film. This won't do, ISO 200 is "slow" film. Light metering it for "correct" exposure in your dim evening light results in the compensation of a slow shutter speed to let more light onto the film. A slow shutter would blur your subject. You need to do something.

What is that something? You decide that film is actually ISO 800 film.  But you don't call it ISO 800, you call it your personal EI 800 film.   Exposure Index is the name for a temporary change of film ISO. But what does this do for you? Well, now that you have EI 800 film, you set your camera/light meter to meter for ISO 800 and get aperture and shutter settings that treat it accordingly. Namely, faster shutter speeds and, accordingly, less blur on your zippy subjects.

Of course, now that you exposed your ISO 200 EI 800 film to ISO 800 settings, if you want any hope of getting a usable picture, you will have to develop it right. That is, you should now develop it as you would any other ISO 800 film. Also, doing this wouldn't be some sort of magic cure for having to get the right ISO film in the first place and would greatly increase grain throughout your picture.

Well, hope that helped a bit. Though, like I said, unless you are taking an actual film photography class I don't know why you should need to know this (you weren't talking about Exposure Value where you? That would make more sense...).

PS. To all concerned parties, this post has a GFI of 3.