Keep throwing punches until the purple energy bar is full and the little glove icon appears. You're now ready for a Power Punch. There are two kinds of Power Punches. The first one is a huge uppercut. The wind up takes a little while, so you are vulnerable to a quick jab.
Power Punches pack a truckload.
Use them to wear down your opponents. Your opponent may see that Power Punch coming and get his block up in time. You worked hard to build up enough energy, so make it count. The second kind of Power Punch is the lunging right cross. This punch does a heck of a lot of damage, too.