I normally think of meaning in terms of isomorphisms between systems.
That is, if we characterize a subset of domain X as entity Ax with relationships to other entities in X (Bx, Cx, and so forth), and we characterize those relationships in certain ways... inhibitory and excitory linkages of spreading activation, for example, or correlated appearance and disappearance, or identity of certain attributes like color or size, and entity Ay in domain Y has relationships to other entities in Y (By, Cy, and so forth), and there's a way to characterize Ax's relationships to Bx, Cx, etc. such that Ay has the same relationships to By, Cy, etc., then it makes sense to talk about Ax, Bx, and Cx having the same meaning as Ay, By, and Cy.
(In and of itself, this is a symmetrical relationship... it suggests that if "rock" means rock, then rock means "rock." Asymmetry can be introduced via the process that maintains the similar relationships and what direction causality flows through it... for example, if saying "The rock crumbles into dust" causes the rock to crumble into dust, it makes sense to talk about the object meaning the word; if crumbling the rock causes me to make that utterance, it makes sense to talk about the word meaning the object. If neither of those things happens, the isomorphism is broken and it stops making sense to say there's any meaning involved at all. But I digress.)
The relationship between the string "2" in a calculator and the number of FOOs in a pile of FOOs (or, to state that more generally, between "2" and the number 2) is different for A and B, so "2" means different things in A and B.
But it's worth noting that isomorphisms can be discovered by adopting new ways of characterizing relationships and entities within domains. That is, the full meaning of "2" isn't necessarily obvious, even if I've been using the calculator for a while. I might suddenly discover a way of characterizing the relationships in A and B such that "2" in A and B are isomorphic... that is, I might discover that "2" really does mean the same thing in A and B after all!
This might or might not be a useful discovery, depending on how useful that new way of characterizing relationships is.
As lukeprog notes, all of this is pretty standard philosophy of language.
So, if asked what "right" means to me, I'm ultimately inclined to look at what relationship "right" has to other things in my head, and what kinds of systems in the world have isomorphic patterns of relationships, and what entities in those systems correspond to "right", and whether other people's behavior is consistent with their having similar relationships in their head.
I mostly conclude based on this exercise that to describe an action as being "right" is to imply that a legitimate (though unspecified) authority endorses that action. I find that increasingly distasteful, and prefer to talk about endorsing the action myself.
I think my previous argument was at least partly wrong or confused, because I don't really understand what it means for a computation to mean something by a symbol. Here I'll back up and try to figure out what I mean by "mean" first.
Consider a couple of programs. The first one (A) is an arithmetic calculator. It takes a string as input, interprets it a formula written in decimal notation, and outputs the result of computing that formula. For example, A("9+12") produces "21" as output. The second (B) is a substitution cipher calculator. It "encrypts" its input by substituting each character using a fixed mapping. It so happens that B("9+12") outputs "c6b3".
What do A and B mean by "2"? Intuitively it seems that by "2", A means the integer (i.e., abstract mathematical object) 2, while for B, "2" doesn't really mean anything; it's just a symbol that it blindly manipulates. But A also just produces its output by manipulating symbols, so why does it seem like it means something by "2"? I think it's because the way A manipulates the symbol "2" corresponds to how the integer 2 "works", whereas the way B manipuates "2" doesn't correspond to anything, except how it manipulates that symbol. We could perhaps say that by "2" B means "the way B manipulates the symbol '2'", but that doesn't seem to buy us anything.
(Similarly, by "+" A means the mathematical operation of addition, whereas B doesn't really mean anything by it. Note that this discussion assumes some version of mathematical platonism. A formalist would probably say that A also doesn't mean anything by "2" and "+" except how it manipulates those symbols, but that seems implausible to me.)
Going back to meta-ethics, I think a central mystery is what do we mean by "right" when we're considering moral arguments (by which I don't mean Nesov's technical term "moral arguments", but arguments such as "total utilitarianism is wrong (i.e., not right) because it leads to the following conclusions ..., which are obviously wrong"). If human minds are computations (which I think they almost certainly are), then the way that a human mind processes such arguments can be viewed as an algorithm (which may differ from individual to individual). Suppose we could somehow abstract this algorithm away from the rest of the human, and consider it as, say, a program that when given an input string consisting of a list of moral arguments, thinks them over, comes to some conclusions, and outputs those conclusions in the form of a utility function.
If my understanding is correct, what this algorithm means by "right" depends on the details of how it works. Is it more like calculator A or B? It may be that the way we respond to moral arguments doesn't correspond to anything except how we respond to moral arguments. For example, if it's totally random, or depend in a chaotic fashion on trivial details of wording or ordering of its input. This would be case B, where "right" can't really be said to mean anything, at least as far as the part of our minds that considers moral arguments is concerned. Or it may be case A, where the way we process "right" corresponds to some abstract mathematical object or some other kind of external object, in which case I think "right" can be said to mean that external object.
Since we don't know which is the case yet, I think we're forced to say that we don't currently know what "right" means.