General Relativity
After spending all this time discussing special relativity, it's only fair to give general relativity some time.
Remember when we talked about time as the fourth dimension? We defined an event as having space-time coordinates of (x, y, z, t). Space-time, then, is simply the unification of space and time. We said at the time that special relativity is special because it ignores gravity.
Without gravity, space-time is flat, an infinite sheet, though in more than two dimensions. However, we have massive planets and stars and galaxies that revolve around each other in defined orbits. If we picture space-time as a type of malleable fabric affected by mass, we'll see that it's not flat around planets and the rest. In other words, gravity curves space-time, just like standing on a trampoline bends the surface. We call this phenomenon space-time curvature.
In the above illustration, space-time is drawn as a malleable grid. Without the effect of gravity, Earth would simply rest on a flat surface, like a rock half buried under the ground on a field. The grid would simply be, well, a grid. Its squares would all be the same size. The curvature of space-time changes the length of each square, depending on the influence of gravity. The closer we get to a massive object, the longer the length of each grid square, or the more stretched a grid becomes. This is a simplified explanation of how physicists measure the curvature of space-time.
In flat space, the shortest distance between two points is a straight line. What about in curved space? Ah, now we get to the meat of the matter.
Since space and time are combined, as mass bends space, time gets stretched too. That's right, time dilation. Space-time curvature causes time to flow more slowly. Mathematically, this is because light has to travel a lesser distance between two points in curved space.
The effects of gravity may also be explained with general relativity. Newton viewed gravity as an attractive force between two objects, such as the Earth and the Sun. Einstein explained the same phenomenon using space-time curvature. The Earth rotates around the Sun following the curvature they each form in space-time.
Both explanations are accurate, but Newton's equations don't hold once we start to deal with super massive objects like black holes, just like his equations don't hold near the speed of light.