Question

can any one give me interpretation of delta function potential

Answer 1

To be correct, the delta "function" is a (irregular) distribution (not a function), so from the physical point of view it only makes sense to talk about it when integrating over it.
You can imagine it as a the limit of a Gaussian, where the width approaches zero while the integral stays constant. (Hence the height gets infinity.)
If it's (delta(x-x')) together with any other function f(x) inside of an integral, the integral just leads to the value of the function at the point x=x', i.e. f(x').
Don't know if this really helps, but in principle I would say it's more like a mathematical trick (or property) then a physical interpretation of it.