Dynamic stretching is different to static stretching. For starters it is done before you commence your exercise, rather than at the end like static stretched.
I personally think it's a bit of a misnomer, I would call it dynamic warm up movement...but I don't get a say so we'll stick with dynamic stretches!
To do a dynamic stretch you pick movements that you will use in the upcoming exercise and move through them at full range. This could include kicking movements, walking lunges or torso twists. What you choose all depends on what exercise you are about to do.
Interestingly many forms of Tai Chi have included something similar in their training for hundreds of years, but they are called "loosening exercises." For a great video, which is very dated, but so beautiful to watch if you know your Tai Chi well, is this one of Master HuangXingxiang performing the loosenings. Although apologies in advance for the music!
If you want to stick to the more modern approach and you've ever wondered if you are doing your dynamic stretching properly this video is a good explanation of how to do it.
Dynamic stretching is the new buzzword to keep yourself fighting fit. You don't have to stretch at his pace, but definitely some good ideas worth incorporating into your workout!