What is NDVI? What is NRG?

We've been working a lot on capturing infrared imagery, and producing NDVI images such as the one above.

What are these images we're trying to make? What do they tell us about vegetation, and why? These diagrams should help to understand what it is we're doing and why these are good ways to analyze plant life.

NRG imagery

We're also interested in producing NRG imagery, where Near-Infrared, Red, and Green are used to compose a picture instead of the usual Red, Green, and Blue. This diagram explains the swapping, which allows us to 'see' infrared as if it were a normal color:

Here is an example of an NRG image: