The Multi-Texture Mixer is used to combine multiple texture maps and a mixing map to a single texture. The mixing map is just a grayscale texture with its values interpreted as heights. Different heights are filled with their corresponding texture maps.
Up to eight texture maps can be combined. They are controlled with resizeable sliders at the Mixer panel. If you move a slider down, lower (i.e. darker) grayscale values are filled with the texture. The little up and down arrows at a slider's edges are used to change its size.
The height coordinates of different sliders are allowed to overlap. Textures with overlapping sliders are mixed with the valence, which is defined by the Mixing Curve. A gaussian bell mixing curve is used by default. It has its highest valence at the center of the slider and low valence at the edges. Use the linear mixing curve to give a texture constant valence over its entire range.
You can make the individual textures tile over the output texture by increasing their Tiling values, which are part of the Map Properties. The Offset parameters control the horizontal and vertical dislocation (relative to the output texture)
You can load any texture from the editor or an image file as the Mixing Map. It is converted automatically to grayscale values, so you can employ colored images. A good mixing map for example is a brick texture with a smooth gradient at the bricks' edges. This allows you to nicely blend between the brick-material and the texture of the mortar between:
Tip: If you want to use the Advanced Mixer in your scripts, call it with the advmix command.