Mathematica is a well integrated technical computing environment that can be used to do
     algebra
     arithmetic
     calculus
     data file reading and writing (understands over 130 data formats)
     geometry
     graphics (2D and 3D)
          animations
          contour plots
          interactive rotate and zoom
          normal x-y, and for 3D, x-y-z plots
          parametric plots
     numeric mathematics
     presentation
          electronic notebooks
          slide shows
          web pages
     programming
     statistics
     symbolic mathematics
     trigonometry
     etc.

One can often type a single Mathematica command to solve a problem that would require much more work using other systems.

Mathematica has over 2000 commands, including

E	base of the natural logaritm = 2.718...
ElementData	give value of specified property for a chemical element
Function	define your own function
HermiteDecomposition	give Hermite normal form decomposition of integer matrix
HypergeometricPFQ	generalized hypergeometric function
Manipulate	make controls to allow interactive manipulation of input values
Pi	3.1415...
Plot	make a two-dimensional plot of f as a function of x
Plot3D	make three-dimensional plot of f as a function of x and y
RandomReal	return pseudorandom real number
Sin	sin function
Solve	solve an equation or set of equations
StandardDeviation	compute standard deviation of list of numbers or function

See Wolfram Mathematica: Features and Mathematica for the Classroom for more information.