Wow! Another thread I feel like I can contribute to.
As Onganju rightly said, it's all about acceleration. IMO, in practical terms that means 'snap'. You have to get the motion of a punch to be loose until the last moment, and then unload all the power- the 'snap'. If you don't do it like that, your punch is just a hard push. Very strong people can still do a lot of damage like that, but smaller people not so much. But you need to get someone to teach you- getting this right in some punches is tricky.
It is often said that most people have an aversion to hitting someone full on, and hold back a little. So they say that, at least initially, you should aim to hit a little way back into the target, e.g. when you go to hit them in the gut, imagine you are going to hit them in the spine. Personally I'm not 100% sure about this- someone else can probably vertify.
What people said about having good, firm contact with the ground is 100% right, as is using hip and shoulder.
With all of these things, I would recommend playing with them to get the feel. Get in front of a heavy bag and do it in an exagerated way plenty of times to make sure your body totally feels it. Then practice thousands and thousands of times over.