Moving window analysis selects a "window" of a set size within a raster, which is shifted cell by cell across an area of interest. First, A focal point (center value of the "window") is selected. In the figure on the left, the value of [21] in the center cell is the focal point, with the eight surrounding cells composing the "window".

Each cell (barring those along the edges-- the edge size is dependent on the size of your window) will act as the focal point as the window moves across the raster. For this analysis, the values of the surrounding cells (including the focal point) are averaged, and a new cell value is calculated in the output raster.