Although a nonprofit organization is a legal entity with certain tax exemptions and possible charitable status, that classification doesn't necessarily mean all reuse would be considered noncommercial.
As indicated in the FAQ for the Creative Commons:
If you are a nonprofit or charitable organization, your use of an NC-licensed work could still run afoul of the NC restriction, and if you are a for-profit entity, your use of an NC-licensed work does not necessarily mean you have violated the term. Whether a use is commercial will depend on the specifics of the situation and the intentions of the user.
As stated below in the Creative Commons wiki documentation for
NonCommercial interpretation, it's not the category or class of reuser, it's the intended use that determines this:
NonCommercial turns on the use, not the identity of the reuser. The
definition of NonCommercial depends on the primary purpose for which
the work is used, not on the category or class of reuser.
In terms of what's considered to be commercial use, the Creative Commons points to a survey they conducted in 2008 on the meanings of commercial and noncommercial use. The Executive Summary of this study indicates that commercial use is generally perceived to be
uses that earn users money or involve online advertising. It's advisable to refer to that survey for more details on the distinction between the two.
In summary: It's not the reuser (i.e., nonprofits or for-profits), but the intended use that qualifies it as either commercial or noncommercial.