When describing my sample, I divide it by the binary variable of interest, which is membership in a certain program for my case.
Since I'm not an English native-speaker, I have quite a primitive question: how do I call the groups (what is falsely described as population group in the diagram below)?
If I understood your question correctly, you're talking about stratification.
Stratification is the process of dividing members of the population into homogeneous subgroups before sampling. Source
Therefore, the term you're looking for is called subpopulation or, more formally, stratum.
strata, it's very formal though, as you stated correctly. The plot is created using a sample, though, and not the entire population. Can I use subpopulation anyway? I fear that it's somewhat misleading or confusing.
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I would first comment that (depending on the exact context you want to present this and related figures in), it isn't strictly necessary to have a label for that axis at all. For example, you could simply rephrase "Member" / "Non-Member" to refer specifically to the program in question (e.g. "[Program Name] Member"). The point being is that the primary purpose of figures is to present a clear and concise description of the data to the audience; I would argue that is perfectly clear just based off of the tick labels without an overall axis label. In some situations, it may introduce unnecessary clutter or complexity to add extra terminology onto the figure to further explain items that are already self-evident. Additional, specific information can always be added in the figure caption, assuming this is for the purposes of a publication or report.
I personally don't see how adding "population group" or a similar generic term actually improves understanding of the information being presented in the plot; the function of this plot is to compare the distributions of age among members/non-members, what does it add to my understanding of that comparison to further communicate the fact that the members/non-members are groups, which is already obvious from the way the plot is presented? More informative would be to eliminate the axis label entirely, leaving the plot as is, and present information in a caption to describe, for example, the definition of group membership, comments on randomization if applicable, etc.
In any case, if you do think it is necessary to have the axis label, I wouldn't bother with something generic like "group" or "indicator" because I don't see how it actually adds information to your comparison. A better label would be something directly related to the program in which membership of is being evaluated. For example, just the name of the program would suffice. Or, depending on the nature of the program and how membership status is defined, something more specific like "[Program Name] Adherence".
sample groupbut that doesn't sound quite sophisticated... $\endgroup$sample groupsounds okay to me (but I'd describe myself as "unsophisticated" so you probably have that right). No doubt there's a more sophisticated term to be found, but personally,sample groupor even justgroupis probably what I'd actually use unless someone asked me to use something else. [On the specific side I could say something like "membership group" but that has potential to be confused with one of its own categories; you could say "membership/non-membership group" but that's rather unwieldy, which brings us back to the unsophisticated but general terms we started with.] $\endgroup$