What does it mean for space to be curved? Moving through curved space is
not the same as driving down a curved road, because when you're moving
through curved space, you think you're travelling in a straight line!
How can this be? Imagine approaching an area of great curvature, which
therefore is very hard to traverse. The easiest way to get to the other
side is to go around, rather than through. Thus the line (which is the
shortest distance between two points, as defined by geometry) of your path
is not straight, but curved. Such a line is called a geodesic.
In our universe, things travel along geodesics of spacetime. Because
these geodesics are curved by the presence of matter, an object's geodesic
will curve inward toward a massive body. We observe this effect as gravitation.
Light, too, travels along geodesics, and its path is bent and curved as
it speeds through spacetime.