Purity is the quality of being uncontaminated. Pure water, pure heart and so on.
Sometimes we find the word “purity” in wine descriptions and reviews. What does it mean? As always different philosophies may give different definition of this quite elusive term.

The WSET, which is my field of interest, cites purity in the first chapter of the Level 2 and Level 3 wine textbooks, under the “Complexity” paragraph, but the matter gets only a few words and it often stems questions from the students.
The Level 3 manual tells us that “simplicity is not always a negative, and not all premium wines are complex: sometimes purity and clarity of expression are what make a wine great, and the presence of oak or tertiary characters (for example) might detract from the quality“. The text does not add anything else to this and that is why many students struggle to understand what purity is in practice.

Breaking down the texbook definition, a wine has “purity” when it is characterized by very clear and expressive primary aromas, even just a few of them, without perceivable secondary and/or tertiary aromas.
Notable examples: high quality Riesling from around the World, high quality Chablis made without oak influence, high quality Gruener Veltliner. If we run the SAT in a manneristic way (more aromatic descriptors = good; less aromatic descriptors = bad), we run the risk of downplaying the quality of these wines because of their limited range of flavors, particularly when they are young. However in some cases the quality in the expression of the fruit more than makes up for the supposed simplicity. Try, for example, a young Polish Hill Riesling by Grosset: for me that’s the quintessential pure wine and it’s great.

The new and revised Level 2 texbook contains more or less the same definition. A big difference lies in the “Identifiable characteristics/Intensity of flavors” paragraph, just a few rows above it. The “Identifiable characteristics” criteria to evaluate wine is not present in Level 3 texbook, although I guess it will be added when the text is revised, hopefully soon.
According to it, a wine does not need to be intense to be good: if it offers identifiable and recognizable flavors (precise and defined strawberry and red cherry for example, instead of generic red fruit) it could still be very good or outstanding, even if its intensity is not pronounced.

The question may arise: does this criteria overlap purity? Not exactly.
A wine with purity has identifiable characteristics, but not all wines with identifiable characteristics are necessarily pure. They may be complex: e.g. we may be having a wine with precise and identifiable primary, secondary and tertiary aromas, like a mature Brunello di Montalcino. In this case the wine is likely high in quality, but it does not fall in the WSET definition of purity.

There may be people using “purity” with a different meaning, for example I have seen it associated with natural wine. It is fine, but it is not the way WSET uses the word. The important thing is to use it properly in the chosen context, having its meaning clear.