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u r v e d S p a c e
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It
isn't space which is curved it's spacetime. When I talk about curved
space I'm not being very accurate. The reason I do talk about curved
space is because it's easier to understand than curved spacetime.
Spacetime is a fusion of space and time; we put the two together because
they are not independent. They may appear to be independent in every
day life but they're noticeably connected if you travel at near light
speed.
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. 

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