Difference between DA and Rotary polisher
Years ago, the vast majority of paintwork polishing was carried out using rotary polishers with wool or foam pad. These polishers are still the mainstay of many body shops and professional detailers and when used correctly they can deliver spectacular results. However they have a risks attached to them and require practice to be able to get the best out of them. Owing to their nature, where the pad spins on a constant orbit, a rotary polisher can develop significant heat on the paintwork which can lead to paint burns in the hands of an inexperienced user.
 
By contrast, a dual action polisher is a much safer tool to simply pick up and use. By dual action, it means that the pad not only spins in a circle, but it also oscillates. This results in a random orbit movement of the pad sometimes such polishes are referred to as Random-Orbit polishers (RO polishers) for this reason. The diagram below highlights the difference between the pad motion of a rotary and a dual action polisher:

The random orbit nature of a dual action polisher means that it generates far less heat than a rotary polisher. It is a more gentle tool so correction work typically takes longer. However it is also safer to use and easier to learn which makes it the ideal beginners tool.