The sun is incredibly massive object and it causes the space around it to bend. This causes the planets to pulled to the sun or the planets move in an elliptical path around the sun. But I don't understand how the curvature in space can cause the pulling or what cause the planets to move in elliptical path?
As this is not closed as a duplicate I will try a simple answer, though the links in comments are adequate.
In Newtonian mechanics one has the planetary bodies which exert a force on each other.
In General Relativity the same planetary bodies distort the space geometry around them, rather than acting on each other.
The force concept is subsumed by the shape in space. If there are no masses then the space is undistorted. One mass distorts the space around it in a calculable way.
Two masses change in concurrence the space such that the trajectory they travel on follows the least resistance path in this distorted space. Calculations show a small deviation from the solution of Newtonian equations and the consequent ellipses, but important enough for satellite paths and navigation. The geometry is still elliptical,except that it is a path through space and not a trajectory at the end of a force field.
Space "geometry"... seems to ignore real cause and effect. See this for another approach: http://metaresearch.org/cosmology/gravity/possiblenewpropertiesofgravity.asp