To understand exactly what "Progressive Overload" actually is, let's break down the definition of this term, and then we can relate it to P90X.
Overload refers to the workload being applied to an individual. Some may refer to this as "progressive overload" which essentially means that you need to continue to challenge your body in new ways in sequential training session in order for the body to continue to adapt and improve over time.
Exercise causes micro tears and damage to the body which is then rebuilt and repaired with proper diet and rest in order to become stronger for future use. In order for this to continue to happen, the body must continually increase its workload in order to continue the adaptation process.
Progression is related to overload in the fact that an individual needs to continue to progress with their training by increasing their workload in a number of ways. Workloads can be progressed in a number of ways such as shortening rest periods, increasing resistance loads, increasing workout durations, etc. all based on an individual's specific training schedule.
When combining all three of these training principles, a highly effective training schedule can be created for an individual based on their goals and aspirations to create faster, stronger and sometimes bigger muscles to perform better and more efficiently or fatigue-resistant.
To then apply this information to P90X, we must use specific examples from P90X. Let us use the very first day of the standard P90X schedule as an example: Chest and Back.
The very first day you begin Chest and Back, the workout should be difficult for you, because you are aiming for maximum repetitions on (mostly) all exercises. You may not even be able to complete all 24 sets! That is fine, because your body is a very efficient machine, and it adapts to stimulus appropriately - assuming you take proper steps for recovery.
Let's say your very first day of P90X, you average 15 pushups and 6 pull-ups on most sets. The following few days, your chest and back muscles will more than likely be very sore (if not, then you must not have pushed yourself hard enough)! During the time when you are sore, assuming you are eating a balanced diet, as well as getting proper amounts of sleep, your body will mimic a construction site, renovating the micro trauma and tears you caused to your muscle fibers from your workout. This may sound bad, but it is actually good for you, and good for change.
During this "construction phase" (refer to "Muscle Confusion" for more information regarding adaptation), your body will not only be burning tremendous amounts of energy (i.e. calories) repairing damaged tissues, but it will be doing so in a way that your muscles will now be stronger and more resilient based on the training stimulus you attacked it with.
Assuming your recovery period has been sufficient, when you return to Chest & Back on Day 8 of the schedule, you should not only be able to do just as many pushups and pull-ups as the previous week, but you can and should do more.
The "should" is important. Because your body already adapted to the "15 pushup, 6 pull-up average" from week 1. In order for you to continue to improve and get stronger, then you must push yourself to do more than you did the previous week in order to elicit more change.