Most people take the word literally and that is exactly what they do, they just warm up the body, which is fine by all means. However, it is not because your body is warm that your joints are ready to go for a fight.
What I often see though is people overdoing it. They stretch, move, warm up, roll and after 20-30 minutes, they are finally good to go.
I don’t know if the problem comes from the actual warm up or that they need to have 30 minutes to warm up before they get going.
The whole principle behind the warm up is to get the body going, especially what needs to be trained. Doing 20 minutes of bike before doing chest and back is a waste of time, and so is stretching right before a hard workout.
When you stretch, you set the muscle up to relax mode. Even worst, if your muscles are tight, stretching them without warming up properly can even cause some type of damage. Dynamic warm up is best, especially for hips, knees and shoulders since it prepares the joints for gradually increasing resistance and a great tool to warm up and get the heart rate going as well as to wake up the nervous system.
Now, some of us don’t have 15-20 minutes to spare on warming up relentlessly before each and every single workout. When time is of the essence, go specific. By example, if you were to do arms workout by alternating the Scott bench for biceps and the close grip benchpress for triceps, grab about 40% of your 8RM weigth and do only 8 reps for each exercises. Bring up the weight to 60% and do the same, than 70% and you are ready to start. Those sets would only count as a warmup and not working sets.