Htet, we have two responses for you

This is too big a topic for a simple answer. An elliptic plane is easy to describe -- in a small region it is just a portion of the surface of a sphere. To understand elliptic space, you must be able to imagine a hypersphere in 4-dimensional Euclidean space -- that's the set of all points that are a unit distance from the origin. I suggest you look it up in Wikipedia:

http://en.wikipedia.org/wiki/Elliptic_geometry

(or in an appropriate encyclopedia) and get back to us with specific questions on points you do not understand.

Elliptic space is a space with positive curvature; examples include spherical geometry (like that of the surface of the earth) and projective geometry. In elliptic geometry there are no parallel lines (think of pairs of great circles, which always intersect)

The name does not come directly from the word "ellipse", but from the same Greek root, meaning "to fall short" [as in the grammatical term "ellipsis" meaning the "..." punctuation mark.

Good Hunting!
-RD