Anti-aliasing is when you make pictures look smoother and less jagged. Anti-Grain Geometry is a special kind of anti-aliasing that is used to make computer pictures look really good without looking blurry or distorted.
Imagine you are drawing a picture in your coloring book. When you color in a shape, sometimes the edges look sharp and pointy. But we want our picture to look smooth, so we need to color the edges too! That means we need to add a little bit of color to the area around the edge so that it looks like the color is fading out.
Anti-Grain Geometry works the same way, except it's for computer pictures. When a computer draws a line or a shape, sometimes the edges can look jagged or pixelated, which is not very pretty. Anti-Grain Geometry helps smooth out those edges by adding a little bit of color to the area around the edge.
It's like when you color with crayons and you blend two colors together to make a nice gradient - that's what Anti-Grain Geometry does for computer pictures. It makes sure that the colors blend together smoothly, which makes the picture look much nicer and cleaner.