Push-Pull is where Nage pushes on Uke in one direction and Pulls on Uke in the opposite direction. There are several places we see this in Aikido. Sometimes in Irimi Nage, Nage will push Uke's head back with one hand while pushing Uke's back forward with the other hand. This has the disadvantage of giving Uke something to resist. Many martial arts do this so it can work but in Aikido we consider it an undesirable, difficult way. In this situation it is best to go to Uke's side and down with both hands.
Another situation where Push-Pull is used is in Ikkyo. Nage tends to lift Uke's hand and push down on Uke's elbow. This gives Uke something that can be resisted. It is best for the force of both of Nage's hands to flow out Uke's arm and toward the floor.
A third example is when Uke holds Nage's arm with two hands. When Nage tries to step in the wrist will pull against one hand and the forearm will push against the other hand. It is better for Nage's hips to drop so that the head can be placed on Nage's hand. This will allow Nage's hands to push against both Uke's hands and then rotate in Uke's hands giving very strong control while avoiding Push-Pull. There are many other examples but this should give the idea.