Welcome to PF;
There is no "why" to how the Universe behaves - it just is.
It's like asking why spheres are round. What we do with physics is try to describe the way the Universe works.
But we cannot tell you
why it works that way or
why a particular model for a class of phenomenon is a better fit than other models - in any deep way - that is just how it turns out.
We can answer in a shallow way - in which we use some framework of things that happen ... but coming up with that framework is what physics tries to do and the best framework for understanding gravity and the related phenomenon that we have right now is general relativity. Why is that framework the best? Because it best fits the experimental evidence and the things we see in Nature. Why? Well - because that's the way it turns out.
See?
But you do manage to ask some easier questions.
The "bend" in space-time is sort-of in the maths - it is to do with the relationship between measurements made in different points of view and has no non-GR equivalent. While you are getting used to it, you can think of the "curvature" as the name given to the kind of maths you need to use ... it is very similar to the kind of maths needed to navigate between places far apart on the surface of the earth.
It
is difficult to visualize - I agree. 4-D thinking is hard. To make matter trickier, the common "rubber sheet" or "stretchy net" picture you are usually given when you start trying to learn about these things can be very misleading so you need to take that with a grain of salt. It's supposed to help you feel more comfortable but if it doesn't, then don't bother trying to make it understandable. You are just going to have to get used to it.
General Relativity solves a bunch of physics problems that are not so easily handled otherwise. One of these is working gravity into special relativity, which people wanted to do because special relativity was already very successful at the time.
General relativity has been very successful too. We use GR, and thus curvature of space-time, to make GPS navigation work. This is similar to using the fact the surface of the Earth is curved in order to do very precise navigation.
See also:
http://en.wikipedia.org/wiki/Tests_of_general_relativity
... for other examples of problems that don't work out without assuming space-time curvature.
Richard Feynman on the difficulty of "why" questions.
Transcript:
http://lesswrong.com/lw/99c/transcript_richard_feynman_on_why_questions/
... it is in the context of magnetic force but has general relevance.