Why and how the masses attract each other? We generally say that the gravitational force acts between the two bodies of some masses. Why and how that force is generated? What is the main mechanism behind this force?
 A: 
Why and how that force is generated? What is the main mechanism behind this force?

Physics does not answer ultimate "why" questions, because it is a discipline which ultimately describes with mathematical models what is observed in nature. The models differ from maps because they not only fit existing data/measurements but are also predictive of new results of experiments and observations. Then the model can be used to see how from one state another state can be predicted or described. The why is contained into the laws and postulates of the theoretical model, which are a distillation of observations/measurements or necessary to identify the mathematical functions with physical measurements .
In gravitation the first successful predictive model was Newton's gravitational model:

Newton's law of universal gravitation states that a 
  particle attracts every other particle in the universe using a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. This is a general physical law derived from empirical observations by what Isaac Newton called inductive reasoning.

Together with the laws of classical mechanics the behavior of masses could be explained , i.e. once the laws are assumed the how could be shown mathematically and the outcome calculated.
Once the microcosm started being explored classical mechanics became inadequate to describe and predict behaviors. Quantum mechanics and special relativity were necessary to describe mathematically and predict results. 
The study of the heavenly sphere by astronomy and later astrophysicists showed that Newtonian gravitational theory was inadequate and General Relativity was proposed for large masses with new laws, but still the existence of mass is an observational fact included in a nested fashion  in the postulates of general relativity.:

The first postulate is the relativity principle: local physics is governed by the theory of special relativity. The second postulate is the equivalence principle: there is no way for an observer to distinguish locally between gravity and acceleration.

The measured mass  concept is nested in the first postulate, as shown in the link.
So the answer to your question of "why" , is because that is what measurements and observations say. The "how" is given by the corresponding mathematical theory of Newtonian gravity or General relativity depending on the dimensions and other boundary conditions of the problem under study.
A: Einstein's theory of relativity states that our universe is essentially made up of a "sheet" of space time.  A body of mass warps this space time and creates a "valley" in it - the more mass a body has, the bigger a "valley" it creates in the space time continuum.
Other masses are attracted to this mass (and vice versa) because they fall into the "valley" in space time that is created.  A planet has more gravitational attraction on you than, let's say, a table, because it warps space time and creates a far larger dent in it.  Hope that helps.
A: Ravi. I'm no expert in general relativity, but it is generally accepted that a massive object warps the spacetime around itself, which will have an effect on objects nearby enough to follow this new curvature to an otherwise flat spacetime. If gravity is ever quantized, like the three other forces of nature, the force carrier of that theory would be called the graviton, and it would be a boson akin to the other force carriers.
