Conditional routing in graphs means starting at a specific node and deciding which path to take next by checking a condition at that node. If the condition is true, you follow one path; if false, another. This continues until you reach an end node, where routing stops. For example, starting at 'start', if the input is greater than zero, you go to 'node1'; otherwise, you go to 'node2'. Both 'node1' and 'node2' lead to 'end', which stops the routing. This method helps in making decisions step-by-step in a graph based on changing inputs.