Gravity bends space?

If gravity bends space (and therefore elliptic trajectories of celestial objects), then why do comets breakup due to tidal forces? Shouldn't they glide (stretching and shrinking) through the space as it is (bent or not)?

What does it mean for space to be bent? What does it mean for objects that exist and travel through that space.

Wtf, guize, I'm confused with relativity theory and all this gravity bends space thing.

nb4 troll. please, discuss.

M'ass used to bend space, but then I went on a diet!