First I’ll start by explaining everything from the beginning about how graphics and textures are rendered onto screen. Then I will go into a bit of detail about anisotropic tri-linear filtering itself.

Aliasing:

This is all about how rendered images can appear jagged at the edges due to resolution.  All images on the computer screen are made up of pixels, the more the better for image quality (its resolution).

Have a look at the below image. It shows a circle in 3 different resolutions (amount of pixels). The first image is a poor representation of a circle and very blocky, this is aliasing. The second and third are much better because of the increased resolution:
 

Anti-Aliasing:

So then, Anti-Aliasing (abbreviated AA) is the technique to try and fix the image quality and reduce the distortion artefacts so that images don’t appear as jagged. It is used to make images look better without increasing resolution by blending the edges to make them appear smoother.

Below you can see two different renders of a 3D Robot Game Character I created: