Well, first of all, it's a computer/symbolic algebra library. Say, are you familiar with SymPy? If so, think of AngouriMath as of something similar, but for .NET. It's .NET, after all, which is going to rule the programming world, not python.
If you don't know SymPy, AngouriMath can be similar to Wolfram|Alpha in some way. You can manipulate so-called symbolic expressions, that is, mathematical expressions written within a normal human notation (aka with functions, operators, etc.), and variables.