Some plants prefer more sunlight than others. Since the sun in the northern hemisphere is in the south, this means that some plants like to live on the southern sides of mountains (more sun) while others will prefer the north side (less sun). The pixels in an aspect raster contain the direction that the land is pointing.
Aspect is computed in a similar way to slope in that a plane is fit through a 3x3 grid of pixels. However it's the direction of the plane that is used for the pixel value instead of the slope.
Below is an aspect raster that was calculated in ArcMap. ArcMap uses a rather colorful palette for aspect rasters.
In the raster below, I've changed the color ramp to be grayscale which makes it a little easier to see what is happening.
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