NLDE stands for NonLinear Algebra and Differential Equations, yes, there is a missing "A"? Not really. NLDE is a mathematical software for symbolic computations with solutions of NonLinear (ordinary and partial) Differential Equations (NLDE). These equations are algebraic in their indeterminates, i.e., the differential equations are polynomials in the independent variables and some (partial) derivatives of the dependent variables. We call them algebraic differential equations (ADEs) and their solutions are D-algebraic functions.
The easiest way to use NLDE in Maple is by putting the downloaded file, NLDE.mla, in your working directory and including the lines
> libname:=currentdir(), libname:
at the beginning of your worksheet.
However, to avoid carrying the file NLDE.mla in all your working directories, you can just put it in a directory that you defined for libraries. For more details about this, please have a look at the Maple help page of libname.