Wittgenstein asks what all languages and parts of language have in common that define them as language. He replies that there is no "general form of propositions." The things we call "language" are indeed related to one another, but they do not all share a defining characteristic. "Language," in this respect is like "game." If we examine all the things we call games, we will not find any one feature in common, but simply a number of relationships between kinds of games. Wittgenstein calls the similarity between different kinds of games a "family resemblance" because a family is also distinguishable by certain similarities in features, but is not defined by any one or number of those features.
This notion of family resemblance might make us uncomfortable: does this mean that words like "game" have no exact definition, or that there is no clear boundary as to what counts as a game and what does not? Wittgenstein replies that we don't always need exact definitions and clear boundaries to make words usable, just as we don't need to define "one pace" as two feet or some such exact measure in order to use the word "pace." Not every aspect of language need be sharp or distinct. Often a word with unclear boundaries is exactly what we need, and attempts to provide sharp definition will necessarily distort its meaning.
We can know what a word means perfectly well without being able to give a precise definition. For instance, in the claim "Moses did not exist," we may mean a number of things by "Moses." We may mean the man who led the Israelites out of Egypt, the man who bore that name at that place and time, or the man who as a child was taken out of the Nile by Pharaoh's daughter. If the story of Moses being taken from the Nile as a child turns out to be false, but all the rest is true, it is difficult to deny that Moses existed. However, there is no set limit for how many or what particular facts about Moses must be false for us to deny his existence. The word "Moses" has no fixed meaning.
To say that a word has a definite meaning is to say that its application is bound by exact rules. But rules in themselves do not provide the certainty we hope they will. Rules can always be misinterpreted, and even if we establish a second set of rules to explain how we should follow the first set of rules, that second set is also liable to misinterpretation. Rules and explanations are not always necessary. Normally, we can proceed without them, and need only appeal to them in cases where there is a danger of misunderstanding. We only need to be as precise or exact as our situation demands of us.
These investigations are "grammatical." We seek to remove misunderstandings that may spring from analogies drawn between different forms of expression, among other things. But we should not think these investigations lead us gradually toward greater exactitude in language. In most cases, language does not need to be more exact than it already is.
As Wittgenstein points out, it is impossible to devise some definition of "game" that includes everything that we call games, but excludes everything that we don't call games. Are all games amusing? Players in a championship football game are not amusing themselves. Are all games played according to rules? Children tossing a ball around do not necessarily stick to a set of rules.