I would highlight Wittgenstein's idea of family resemblances, which served as a basis for a very productive field in semantics (specificaly prototype theory). This basically postulates that words and their meanings do not work in binary categories but are organised in a field-like manner, where at the centre of the semantic field you have the prototypes (the most typical exemplars of something) while towards the edges, you have the less clear exemplars.
E.g.: semantic field of furniture - table is a prototypical example of furniture, a lamp is a solid one too, a TV is not a superb one but still passable, computer not so much, alarm clock is a bad example of furniture, etc.
This goes very far and basically gets rid of almost any defining features that would trivialise the category to a binary choice - e.g. "adoptive mother" is still a kind of a "mother", much more so than for example a "vacuum cleaner" even though the term specifically denies the biological relationship in the family.