You're right, the continents are moving. Actually, the continents are parts of larger plates that make up the Earth's crust. These plates are shifting around at rates on the order of millimeters per year.For example, here in southern California, the plate under the Pacific Ocean is sliding north along the edge of North America. Because the rates of movement are so slow and the Earth's surface is so large, it takes a long, long time for a super continent like Pangaea to form. Tens of millions or hundreds of millions of years in fact.

There are some places on Earth today where continents are colliding. You've heard of the Himalayas? The Himalayan Mountains are forming as India moves north into Asia, causing the Earth's crust there to fold and push up into mountains. It's possible that more continents will collide to form a super continent sometime in the far, far future.

The continents are continuously moving at the rate your fingernails grow--a few centimeters a year.

Pangaea is the name of the most recent super continent. Take a look at a map of the word that includes topography of the oceans, and you'll see what looks like a submerged mountain range in the middle of the Atlantic. This is one region where the continents are spreading apart from each other.

While the continents will probably never look exactly like Pangaea again, they will inevitably form a super continent again, and scientists predict that the next super continent will form in the next 200-300 million years (it's hard to predict, since we have to assume that the current movement of the plates will not change with respect to each other).

Earth's tectonic plates are constantly moving -- just like you heard -- at about the same rate our fingernails grow. That amounts to, at most, a few inches per year.

Geologists think that sometimes the continental crust is all pretty much in the same part of the globe (like Pangaea) or split into a lot of different continents (like now). They call this the Super Continent Cycle.

The last time Earth had a super continent was ~200 million years ago when Pangaea broke up. The time before that was ~580 million years ago --geologists call that one Rodinia. In another ~250 million years the Earth will probably have another super continent.

Check out the Paleomap Project to see pictures of what geologists think the Earth looked like through time and how it will look in the future.
Paleomap

Cheers

What you heard is only partially true. The continents are not reforming Pangaea, but the tectonic plates are in constant motion. In some places there is new material coming up from beneath the crust - in the mid-ocean ridges. In other places there is crust that is being pulled down under another piece of crust - we call those "subduction zones" such as under Japan. In still other places, plates are just slipping past each other -we call those transform faults. The San Andreas Fault is an example of this.

So, the continents are not reforming back into another super continent,they are constantly moving around on the surface of the earth, carried along by the motion of the larger tectonic "plates." If you want to learn more about this, you can go to the web page of the Geology Department at UCSB,
Geology animations; look at these animations of plate tectonics by Professor Tanya At water.

They will never form the same Pangaea that existed 200-250 million years ago, because the continents will be attached to each-other in different places. Antarctica and South America are currently moving away from other continents, not toward them, and east Africa is splitting off into the Indian Ocean. However, the rest of Africa, Europe, Asia, Australia, and North America will be a continuous land mass within the 25 million years.