Cellular automata are self-generating computer graphics movies.
The net effect of the individual updates is that you see an ever-evolving sequence of screens. That is, we think of all of the updates being done at once. Locality means that when a cell is updated, its new color value is based solely on the old color values of the cell and of its nearest neighbors. Homogeneity means that each cell is updated according to the same rules. Typically the color values of the cell and of its nearest eight neighbors are combined according to some logico-algebraic formula, or are used to locate an entry in a preset lookup table.