There are a lot of different ways to improve your explosion and quickness, but the best way to do so would have to be the use of plyo-metrics. Plyo-metrics vigorously train your fast twitch muscles, which in return leads to improved quickness and explosiveness.  These exercises can help you run faster, jump higher, throw a faster jab and just become more powerful.  There are upper-body and lower-body plyo-metrics, so you can train total body, or be specific with which part you want to train.  You have to make sure you stretch well when doing plyos because there’s a risk of straining muscles.  You have to do plyos at a fast speed to improve the fast twitch muscles.  Here are some examples of plyo-metrics broken down by upper and lower body...

Examples of Upper-body Plyos:

• Clap pushups- do a regular pushup but at the peak explode your hands off the ground and clap, then catch yourself and keep going for a set.
• Line Pushups- Find a line or pretend there is a line splitting your hands in push up position.  Then throw your body from side to side having the opposite hand touch the line each time.
• Medicine Ball Clap Pushups- Start in push up position with a medicine ball between your hands.  Explode into a clap push up, but land on the medicine ball.  Once you land on the medicine ball, do a close-grip push up on the medicine ball, then drop hands back on the floor to regular push up position and repeat on the opposite side of your body for your number of repetitions.

Examples of Lower-body Plyos:

• Bench Jumps- Simply stand next to a bench and jump onto it as fast as you can.  You can change it up by facing the front, back, or the side of the bench to work different twitch muscles.  Also, if you become advanced you can rotate your body in the air, or go side to side to work on agility and balance, as well as improving fast twitch muscles.
• Speed Skater- First, start with legs shoulder width apart, jump and explode out to the right as far as you can and land on your right foot.  Try to quickly make the weight transition and explode as far as you can to the left to complete the exercise.  Do this for your desired number of repetitions.
• Knee Tucks- Start out standing with feet shoulder width apart.  Hold your arms straight out with your palms facing the floor.  Jump as high as you can and at the summit of your jump snap your knees to your palms as quickly as you can.  Do this for your desired number of repetitions.