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You may have heard somewhere that the moon is gravitationally attracted to the Earth. This is indeed true. But then the natural question is... why doesn't the moon just slam into the Earth one of these days?
Here's an intuitive explanation for what in the world is going on. (No pun intended.) The moon has some momentum right now; if gravity just suddenly stopped working, it would go flying off into space in a straight line perpendicular to the "invisible rope" connecting it and the Earth. But the moon will continue "falling" towards the Earth due to gravity, so it is basically just falling around the Earth in its orbit. Importantly, none of this would work if the moon did not have its initial momentum.