There are actually two different implementations of Numerical Python: the original one, "numeric", which is reasonably complete and stable, and a new implementation, "numarray", a complete rewrite of Numerical Python that is not yet complete and stable (as of November 2003). The differences, while substantial, are implementation details; the rest of this discussion applies to both.
Because Python is an interpreted language, mathematical algorithms often run much slower than they do in compiled languages like C or even Java. Numerical Python addresses this problem for many numerical algorithms by providing multidimensional arrays and lots of functions and operators that operate on arrays. Thus any algorithm that can be expressed primarily as operations on arrays and matrices can run almost as fast as the equivalent C code.
Some see Numerical Python as a good free alternative to MATLAB, since MATLAB's programming language is similar in some superficial ways to Numerical Python: they're both interpreted, and they both allow you to write fast programs as long as most operations work on arrays or matrices instead of scalars. Right now MATLAB has the mathematical advantage in that it has many thousands of built-in mathematical functions and many more available as commercial products, while Numerical Python has the advantage that Python is a more modern and complete programming language, and it is also open source.