1) Prevents injury: warm up makes muscles, joints and ligaments more flexible.
2) Mental focus: warming up for 5-10 minutes before your workout will set your mind straight on a task, which will increase your productivity during the workout.
How to Warm Up Effectively
1) Light Cardio: doing 5-10 minutes of a light cardio exercises (walking, cycling) will get the blood flow going and will elevate your heart rate. Just like before driving a car that had been standing in the cold, you need to warm up the engine first.
2) Dynamic Stretching: dedicate about 5 minutes to such warm up drills as leg swings, arm circles and trunk twists. Every stretch like this will warm up the individual muscle and will prepare it for the activity.
3) Practice Exercises with Light Weight: Say, you are working your lower body today, and the first exercise is the squat (I hope it is!). Practice the movement without the weight first to mentally prepare yourself for the exercise and warm up the muscles that are used in that particular movement. Do it before each exercise.
Sample Warm Up
Step 1: 5 minutes walking on a treadmill
Step 2: 10 front leg swings and 10 side leg swings on each leg
Step 3: 10 trunk rotations on each side
Step 4: 10 front and 10 back circles with arms
Step 5: 20 body squats.
The warm up is also very effective in the morning, just after you wake up. It will eliminate stiffness and will prepare you for the day.