You have already been given a number of great answers that will lead you to an entirely new set of questions, but it seems that no one has mentioned either Sellars's or Brandom's account of meaning yet, so I thought I should mention them. Generally speaking, both claim meaning is ultimately bound up in linguistic activity, although they differ in some regards as to what this actually means.

Sellars:

When given the question "What is meaning", we intuitively think (at least I'd like to believe this intuition is widespread) that meaning is a type of word-fit-world relation, which is to say, more simply, we adopt a sort of view in which the words we use are descriptions of the world that we all share through our similar perceptual experiences. We can alter this slightly and say that, intuitively, we think meaning works in the way John Locke has expressed that language does: words help to signify the ideas we already have in our minds. This means we ultimately abstract certain objects or 'types' from experience and turn those abstract ideas into words for general and common usage. Is there anything wrong with this?

According to Sellars, this conception of meaning, broadly construed, is not adequate. As many note (henceforth not only Sellars has noticed this issue), if the aforementioned theory of meaning and Lockean picture of language is correct, where do words like 'and' 'but' and 'if' fit into this? These words have meaning sententially, but independently they do not seem to pick out any object in the world, so there is surely something missing here.

Second, Sellars says there is more to meaning than just a word-fit-world relation (though there still *is* such relation). On Sellars's account, meaning is bound up functionality: words play functional roles in linguistic practices. More particularly, meaning discourse for Sellars is actually the means by which we tell others (and ourselves) how to use certain expressions. Certainly, this means that meaning now has a normative component to it. So, for Sellars, meaning is reflective of the discursive practices individuals engage in, and even in their practices of thought and action. What Sellars has done here is, in some sense, change or expand upon the sort of "relational" theory of meaning, in which words relate to or correspond to certain states of affairs in the world. In addition, he is now saying that, also, words or expressions have rational relations to each other.

Brandom

For Brandom, the picture is slightly different, although he also rejects the broad view that meaning is a word-fit-world process. For Brandom, the meaning of an expression can be explained inferentially; that is, it can be explained in "the game of giving and asking for reasons." (Note: for Brandom, giving and asking for reasons is a normative practice) Broadly construed, this is akin to Wittgenstein's claim that meaning is use. The meaning of an expression is how one uses it, and because one uses expressions within the game of "giving and asking for reasons" there is a normative standard they have to meet; for if they were to use an expression incorrectly, their audience could reject the veracity of their claim and demand that they re-state it, for example. In some regard, this means that in order to identify the meaning of an expression, one has to make assertions--i.e. give reasons for X or P-- and be able to defend (or 'justify') their assertion. For Brandom, this should be understood in terms of inference or reasoning because expressions and assertions take place within, as you might guess, the game of giving and asking for reasons.