It's a reaction that CAN occur between your starting material (either one or more of the components of the reaction) but you don't necessarily want to occur. Say you put A and B together and throw some C in there to help them react, but if you have too much A, then A+A could react or A+C could react to make something different other than the AB that you want. Anything that causes a product other than the desired to form is considered a competing reaction.