What I recall of my school science usually referred to gravity as one of the four main forces that worked between objects in the universe -- they were electromagnetism, the strong nuclear force, weak nuclear force and gravity.
Big objects have more gravity than smaller objects, we learned, which is why small objects in space either crash into the bigger objects or fall into an orbit around them. The bigger objects exert more gravitational force. Only it turns out, as Albert Einstein figured out in 1916, that gravity isn't really a force between objects at all. It only seems to be, because we perceive three dimensions of space instead of the four dimensions of space-time. We experience time's passage, but we don't really perceive it the way we perceive height, breadth and depth. In four dimensions, gravity can be seen for what it really is: the curvature of space-time.
The most common illustration of what this means is picturing a bowling ball or something heavy, resting on a trampoline. A small marble rolled in the ball's direction will curve towards it because the bowling ball curves the surface of the trampoline. The more massive the ball, the greater the curve.
So what Einstein theorized and what scientists have found evidence of is that when objects move through space-time, they create little gravity-wave ripples in it. And as the article linked here notes, I do mean little. The best theories about gravity waves is that the strongest of them -- created when two black holes collide, for example -- would move a subatomic particle a distance of one part in 1,000,000,000,000,000,000,000. This number is called "one sextillion," if you're curious.
This is why they are hard to find, and why only recently have scientists been able to devise experiments to try to measure them directly. They want to do this because gravity waves could be keys to measuring what physics are like in really weird places, like black holes, as well as measuring oddball structures that might make up the universe, like superstrings.
Chances of surfing such waves are remote, of course. For one, they move at the speed of light, which makes it hard to keep up with them. And for another, as mentioned above, they are very small. If they're only going to move a subatomic particle 1 in one sextillionh of a degree, the chances are slim they'll propel you and your board anywhere when they do.