'Nanopure Water' is water purified using a Barnstead/Thermolyne Nanopure lab water system. Over the past 30 years there have been several different Nanopure water systems and each can have up to 4 different configurations. 
The term Nanopure water usually comes from a procedure written in a laboratory that had a Nanopure water system and instead of calling for Type 1 water or some other water specification, they simply called it based on the equipment available in the lab of whom ever wrote the procedure to begin with. The basic Nanopure produced water meeting NCCLS, CAP or ATSM Type I water, having 18.2 megohm ionic purity with little, if any bacteria. 
Other versions can also give ultra low total organic contamination (UV) and Pyrogen free water (UF) or a combination of all of the above. The different Nanopure systems were knows as the Nanopure II (oldest), Nanopure Bioscience (aka a quad) and the Nanopure Diamond (most recent version). 
You will also find the same thing called 'Milli-Q Water' or DI water but all of these terms are vague when discussing the actual water quality needed for a given procedure.