A theory explaining gravity as an inertial phenomenon in curved space.
Gravity is caused by movement of the universe in respect to higher dimension(s)
and can be explained by generalizing basic wellknown laws of physics.
Inertial theory of gravity is an attempt to simplify and demystify gravity. Modern physics admits that gravity is very different from other forces (strong, electromagnetic and weak) and perhaps less understood. Newton first described and formalized effects of gravity. Einstein made a significant step in understanding its nature and improved the way we can estimate it. Still, we cannot really tell what causes gravity and why it is so special among other forces. Calling it a “field”, a “universal force” does not help explaining it. (Don't even start about the gravitons).
I'm attempting to provide a simple (as possible) explanation of what causes gravity.
Our knowledge of the world is and always will be partial – being a part of a whole, we cannot contain knowledge of the whole. Every theory, even the one considered “correct”, is wrong. However we still should try to explain essence of the things in a way that will match our world as close a possible. At the same time, our explanation should be as “simple” as possible (I'd really like to refer to socalled “Occam's Razor” here).
Considering the statement above, I believe that inertial theory of gravity explained here is “true” or “correct” at least to a certain extent.
We live in a threedimensional universe. We are able to perceive width, height and depth. When science attempts to describe behavior of objects, it always does it in respect to three dimensional space.
Several theories, including the popular “Big Bang” theory, consider our universe as being a fourdimensional object (I personally prefer 4D sphere to any other forms – again, for sake of simplicity). The Big Bang theory also considers it expanding, i.e. radius of the 4D sphere is increasing.
I believe it will be a valid assumption that, besides expansional movement there also can be other kinds of movements : linear (or circular, or elliptic, etc.) and rotational movement. All of them (even expansional one) should be considered with respect to higher dimensions.
If universe moves in n dimensions along the straight line and with constant speed, it will not affect objects in the universe (generalizing Newton's law). I would also suggest that if universe moves with some acceleration but it accelerates in direction “orthogonal” to the universe, objects in the universe will not “perceive” this acceleration.
Let's look at the lowerdimension analogy.
Fig. 1.1 
Suppose that we have twodimensional universe (Fig.1.1), which moves with acceleration in direction “perpendicular” to the universe (projection of the vector on the universe's plane is zero). In this case flat “apple” behaves as there was not any acceleration at all (some extra details on that in chapter 4).
Fig. 1.2 
In the next example (Fig.1.2) same universe moves with acceleration oriented in some other (nonperpendicular) direction. Now projection of the acceleration on the universe's plane is nonzero (vector ). This results in apparent movement of the “apple” with acceleration in respect to the universe.
Einstein suggested that space is curved in vicinity of massive bodies. Unfortunately, I cannot suggest anything except rather intuitive notion of “space fabric”, which bends because of certain reason. However I suggest that reason for such bending is quite analogous to what would happen to the real fabric, if it had a massive object on it and the fabric moved with acceleration directed perpendicular to the fabric's surface.
Again let's look at our twodimensional analogy of the universe.

Fig. 1.3 
The universe moves along the perpendicular to it with acceleration . Because of this, massive objects “bend” the universe in the direction opposite to the vector of acceleration.
Let's forget for a moment about what could cause a universe to accelerate continuously, we'll talk about it in the next chapter.
Now take a closer look at what happens in vicinity of the massive bodies, where space is curved.

Fig. 1.4 
We're taking step forward from our simplified view on Fig.1.1. Here (Fig.1.4), we take into account space bending. In vicinity of a small body (small “apple”) projection of the acceleration vector on the space is nonzero, which causes small objects “slide” towards the massive ones (here we do not consider space bending caused by the small objects themselves and effects caused by that). Compare this with the case pictured on Fig.1.2.
Now, what could cause our universe to constantly accelerate? Big Bang expansion itself does not stand as such a cause for acceleration – in the universe's lifetime (which is estimated several billion years) the speed of expansion would build up an impossibly huge value. From the reallife experiences, the easiest way to get a constant (and powerful, if needed) acceleration is to use circular (rotational) motion. So I suggest that universe (which is supposedly a four dimensional sphere) rotates around fifth dimensional axis, and this axis is orthogonal to 4D hyperplane which includes our universe. I'll try to explain it with onedimensional analogy of the universe.
Suppose we have a one dimensional universe – a line (cannot really draw an apple – just a red segment).

Fig. 1.5 
“Finite, yet unbound” version of such a universe will be a circle (twodimensional “sphere”). In order to rotate it in a fashion that will provide equal acceleration for every point of a ring, we should spin it about the third axis:

Fig. 1.6 
So here we have 1dimensional “universe”, bent into 2dimensional “hypershpere” rotating about 3dimensional axis, orthogonal to the plane which contains the “universe”.
We'd already have troubles drawing a picture of twodimensional universe case – it will be represented by sphere (3Dobject already) rotating about the fourdimensional axis orthogonal to the “hyperpane” of the sphere. Please note, that if we rotate it about any threedimensional axis, we'll get different rotational speeds for different points of the sphere (just imagine a rotating globe).
As a conclusion we have the following:
Our universe is a fourdimensional hypersphere, which rotates about a fivedimensional axis which is orthogonal to a hyperplane containing the universe. The rotation creates centripetal acceleration, which is generally orthogonal to the universe's space in every point (and not perceived by the objects of the universe*). However, the centripetal acceleration causes curving of the space in vicinity of massive bodies. As a result, in the curved areas the acceleration is not orthogonal to the space, which appears to the universe's objects as gravity.