It is possible to take the notion of “family resemblance” and make into something that competes with the notion of “definition.” That would give us the first understanding of the notion. Accordingly, concepts (all concepts or some concept) don’t have this structure, but that structure: they can’t be exactly captured with a single definition, but only with a cluster of definitions. We may now imagine the definitions as rings covering areas, and put them one on top of the other, and this may make our concepts look blurry around the edges, where there is less overlap between the rings. But the point about blurriness is separate.
This is however not the best way to understand what Wittgenstein means by “family resemblance.” It is actually quite bad, for it misses the whole point of his introducing this concept. The purpose of introducing this concept is not to help us improve our ability to define. It is rather to make us look: To give us a tool for looking (to draw contours, rather than barriers. For more on this distinction see here).
The purpose of a definition is to replace our natural understanding (e.g. because it is not scientific, not exact): Think of the scientific understanding of “red,” or the legal definition of “marriage,” or the medical definition of “alive.” Think how those definitions give us things that are different from what we get with our natural use of those terms. A definition sacrifices some of the reasons for having a concept for the sake of uniformity. (Which is not to say this is necessarily a bad thing. For some purposes (scientific, legal, medical), uniformity is indeed useful.) Now, a cluster of definitions does something very similar. In fact, it can be thought of as an improvement on what a single definition can do. True, it makes things look more complicated. It gives up on the singularity, and pays the price of simplicity. But it gains in exactness. A cluster of definitions can capture much more than a single definition can.
As opposed to giving a definition, we may rather want clarification or characterization. And this will give us the second way of understanding what family resemblance is. Let me put family resemblance aside for a moment, and explain what I mean by “clarification.” Suppose someone clarified the notion of ‘marriage’ thus: “It is not marriage if you don’t let it change you.” This can allow us to see a face of marriage. It is not a definition; it involves no notion of boundaries--not even blurred boundaries! The Fregean comparison of a concept to an area, which Wittgenstein mentions in PI §71 just does not apply. It rather allows us to get a proper feel for, or to get us to think about, what we need that concept ‘marriage’ for in the first place, and how our world would be poorer without it. It allows us to consider what conceptual life a part of reality in which we live demands. It allows us to get attuned to a web of interest and sensitivities, and to a network of particularities and detail which permeates the encounter between mind and world. My point is that the same kind of clarifying effect can be had when we look at different ways of using a concept: when we look at the family resemblance of the different uses. It is a fact about us that looking at something together with something else, alongside an object of comparison, often helps us to see it better. And I take it that the idea of ‘comparison’ is internal to the notion of family resemblance: We learn—come to see—what a concept means by comparing what it means in different cases, putting the different cases alongside each other.
It is useful to note that when comparing things in this way, we do not have to put them one on top of the other (as opposed to alongside one another): like the different definitions of a concept mentioned above. That is, to see a family resemblance is not typically to produce a Galton-style picture, which morphs the different cases, and brings out what all have in common. Imagine comparing different shades of red in this way. There would be nothing in common to all the shades. Although I don’t want to deny that a family resemblance may be made visible in this way in some cases, it can also be misleading to portray it in this way. For although a resemblance is something that we see, resemblance is not a visible object. It is a (grammatically) different kind of object of sight.
A note about aspect-perception: Wittgenstein sets the stage for a discussion about aspect-seeing, in section xi of the second part of the PI, with a discussion about seeing similarity. He says there that it involves a special kind of object of sight. If I’m right about family resemblance, executing the philosophical method or methods of looking for family resemblances, which Wittgenstein recommends in the first part of PI, involve the ability to see aspects. The ability to see aspects is not the ability to engage in a practical routine. (I discuss the distinction here.) Nevertheless, seeing an aspect can make a practical routine visible.