Dynamic stability is the overall tendency of an airplane to return to its original position, following a series of damped out oscillations. Dynamic stability is how an airplane responds over time to a disturbance. And it's probably no surprise that there are three kinds of dynamic stability as well:
Positive Dynamic Stability
Aircraft with positive dynamic stability have oscillations that dampen out over time. The Cessna 172 is a great example. If your 172 is trimmed for level flight, and you pull back on the yoke and then let go, the nose will immediately start pitching down. Depending on how much you pitched up initially, the nose will pitch down slightly nose low, and then, over time, pitch nose up again, but less than your initial control input. Over time, the pitching will stop, and your 172 will be back to its original attitude.
Neutral dynamic stability
Aircraft with neutral dynamic stability have oscillations that never dampen out. As you can see in the diagram below, if you pitch up a trimmed, neutrally dynamic stable aircraft, it will pitch nose low, then nose high again, and the oscillations will continue, in theory, forever.
Negative dynamic stability
Aircraft with negative dynamic stability have oscillations that get worse over time. The diagram below pretty much sums it up. Over time, the pitch oscillations get more and more amplified.