In a nanoparticle, both phase and compositional purities have to be assessed.
Phase purity accounts for the number of different crystalline phases of the same composition which can be detected in the material. For instance, TiO2 can be prepared in at least three different atomic arrangements which present wildly different properties, namely rutile, anatase and brookite. The detection is subtle as the chemical composition is identical, thereby requiring specific characterization techniques like X-Ray Diffraction or Photoelectron Spectroscopies. The empirical formula only tells a part of the story.
Compositional purity accounts for the presence of other, usually undesirable moieties like contaminants. These can be inert for some applications while critical for others, even in trace quantitites, and despite being intrinsically impossible to avoid they must be minimized. The origin can be usually traced to the raw materials, processing cross-contamination, environment, handling, pipework and container corrosion or abrasion.
Knowing the application and the nanomaterial goes a long way in preventing any issue related to purity.