Generally speaking, the body is made to handle various movements, whether it is fundamental or something new that it has to adapt to. It is composed of over 500 muscles for these movements and these muscles are broken down into prime movers and stabilizers.
The stabilizers are always activated based on which position your body is at; even at rest they are still working. The prime movers, on the other hand, aren’t always active. Their main functions spend a long period of time not being used. When muscle groups aren’t being used frequently, less heat and blow flood runs through them, which makes them tighter or less flexible, and more prone to injury.
When we think about exercising, both the body and heart have to be prepared before entering bouts of stress. Therefore, running through some fundamental active warmup helps the body get more flexible from the increase in blow flow, increase in body temperature, and increase in oxygen. As the heart rate increases, the oxygen load increases in the bloodstream, allowing the muscles to better handle tension as they contract and relax - thus preventing potential injuries.
A good active warm up can also serve as a great pre-workout that mentally prepares you for your session.