Warming up prior to a workout prepares your body, muscles, joints, brain, heart, and nervous system for the workout to come.
There are two components to a warm-up; general and specific. A general warmup helps increase your body temperature, redirects blood flow, increases heart rate, which increases your oxygen carry capacity, and improves overall performance. This would include activities such as jogging, biking, and jumping rope. A specific warm-up helps prepare you mentally and physically for the specific movements that will be performed during the workout. This part of your warm-up focuses on safely preparing your joints, muscles, and nervous system, while reducing the likelihood of injury. This would include range of motion, motor recruitment, and functional movements that mimic the workout routine (or sport). So, if your workout includes pushups and once you've completed your general warm-up add in specific movements such as shoulder motilities and a pushup progression drill to fully prepare your body inside and out. This will take roughly 5-15min depending on the activities you have planned.
American College of Sports Medicine (ACSM) explains: "Think of the warm-up as an on-ramp to a freeway. The on-ramp gives you time to bring your vehicle up to the speed of traffic to avoid an accident. The faster the traffic is, the longer the on-ramp should be. In the same way, your warm-up should be longer if the intensity of the conditioning phase is high."
MS, CSCS, NTC, FMS