Leading indicators signal future events. For example, the yellowish-amber traffic light tells you that a red light is coming. A second leading indicators would be building permits which signal you have permission to go ahead and build something. And lastly, bankruptcies.
Lagging indicators follow an event. For example, again with the traffic light, the yellowish-amber light follows the green light. Another example, the most popular example, is unemployment because if the unemployment rate is rising it means that the economy is failing. Interest rates are also another good example because the rates change after severe market changes.
Coindicent indicators occur at approximately the same time as an event. Continuing with the traffic light example, a green light is associated with the pedestrian walk signal. For personal income, a high personal income means a successful economy. Non farm payrolls is another example of coindicent indicators.