SLI stands for Scalable Link Interface. It is the term that Nvidia uses to describe the use of two or more graphics cards connected together by a cable to speed up the rendering of graphics output. It is usually used by games to help provide enough frames per second (FPS) to keep the video images looking smooth.
Using two cards in SLI allows the video system to generate nearly twice as many frames per second compared to using a single card. However, in order for it to work properly, both graphics cards (a.k.a. GPU's) need to be of the same type and speed.
The same thing is possible using two or more AMD based graphics cards except that the term used by AMD is Crossfire X or just Crossfire. The requirements for Crossfiring two or more AMD based graphic cards are similar but Crossfire is not exactly the same as SLI.
Because SLI and Crossfire are separate standards developed by two separate companies, they are not compatile with one another. However, it is possible to use graphics cards from both companies in a single system but they will operate completely separately so there are very few reasons for doing this if any.