A one-dimensional (elementary) cellular automaton consist of a row of cells. Each cell can be in, say one of two states - state '0' and state '1'. At each step there is a rule to update the state of each cell, say based on that cell and its immediate left and right neighbors.
The table below is a representation of the rule for this kind of cellular automata. It is a kind of lookup table. The top row contains all possible state combinations for a cell and its left and right neighbor at step n. The botom row specifies the state of that cell at the next step in each of these cases.