Do words have meanings. In short, yes; but technically, no. When I say "tree" you may think of this.
But what if I said "trunk"? Would you think of this?
Probably not. At least not initially, because I already tricked you into thinking of "trunk" in the sense of how this word is connected to a "tree". Sorry. No more tricks. I promise.
From this short illustration, we already see that a single word can be used to describe/denote multiple entities (e.g. tree "trunk", elephant "trunk", car "trunk", or what about the saying you got junk in yo trunk?—yes, I went there). All of these various meanings are signaled by whatever context they are used in. There is not some special resevoir within the phonological soundbite "trunk" that unleashes a flurry of felicitous meanings. No. Context elicits specific meanings when this word is used.
Sometimes of course multiple meanings might be alluded to at the same time (e.g. would you look at the junk in that elephant's trunk = that elephant has an unusually large butt, or literally speaking—with humor—trunk/"nose").
The point, though, is that "trunk" does not come pre-packaged with these four meanings that I've referenced above. In fact, "trunk" as a reference to someone's behind probably wasn't even a part of "trunk's" standard repetoire of denoted entities in your lifetime (unless you're a 10 year reading this post). "Butt-trunk" is a new meaning of "trunk" that did not spontaneously appear one day in "trunk's" bag of meanings (like Scott Calvin pulled from Santa's bag), but is a meaning that developed over time through consistent use in a specific context in which it became natural to refer to one's bottom simply as one's trunk. In other words, this new additional meaning came about through context, context, context. It did not magically appear or always exist as some untapped semantic resource until this point in history.
Another simple example is the word "like"—it's not hard to see how Facebook has transformed the traditional meaning associated with this word.
Now I've tried to keep things simple—some will of course say too—but at this point I want to give you something to chew on. It's an excerpt from an article of a "real" linguist (Evans, V. "Lexical concepts, cognitive models and meaning-construction," Cognitive Linguistics 17:4 , p. 492), one who specializes in lexical semantics (i.e. what words mean, or rather what meanings are "had" by words). I will italicize the central notions:
That is, the ‘meaning’ associated with a word in any given utterance appears to be, in part, a function of the particular linguistic context in which it is embedded. Put another way, word ‘meaning’ is protean, its semantic contribution sensitive to and dependent on the context which it, in part, gives rise to (Croft 2000).
To illustrate consider the following ‘meanings’ of fast .
(1) a. That parked BMW is a fast car.
b. That car is travelling fast.
c. That doddery old man is a fast driver.
d. That’s the fast lane (of the motorway).
In each of these examples the semantic contribution of fast, what I will later refer to as its informational characterisation, is somewhat different. In (1a) fast has to do with the potential for rapid locomotion. In (1b) it has to do with rapid locomotion. In (1c) it relates to ‘caused’ motion beyond an established norm: a speed limit. And in (1d) fast concerns a venue for rapid locomotion. Examples such as these show that the view of open class words, as possessing fixed meanings, is untenable on closer scrutiny. The precise semantic contribution of any word is a function of the utterance context in which it is embedded, and, moreover, the sorts of (conceptual) knowledge these lexical entities provide access to, as I shall argue in detail. In other words, words don’t have ‘meanings’ in and of themselves. Rather meaning is a function of the utterance in which a word is embedded, and the complex processes of lexical concept integration, an issue which is developed below.
With this said, it might be easier to understand now why, technically speaking, one can say "words don't have meanings, meanings have words."
Having gotten so deep into all this, one who studies the Bible might wonder: So what's the big deal with having such a nuanced understanding of the relationship between words and meanings? While there are many, and please do chime in below in the comments if you can think of more, I see one elephant in the room.
If I approach some theologically loaded word with some preconceived idea of its meaning (that maybe I got from a systematic theology book or sermon), and everywhere I see this word in the Bible I bring along this particular meaning and assert its presence, then chances are I'm doing myself and the text a great deal of harm by "flattening" the actual message of the text.
For example, if I hear that the Hebrew word for "spirit" is the same one used for "breath", and decide that in Job 7.7 when it says my life is but a breath that "the actual meaning" is my life is but a spirit then I've done more isogesis than critical exegesis—and really introduced a foreign concept to the text. (This is a very clear mistake, but more nuanced misreads certainly occur; they're just harder/takes longer to illustrate).
Let's wrap it up now: if the meaning of a word is dependent upon the context in which it occurs, then it makes a lot more sense to pay close attention to the context than to lug around any pre-defined notions of the word. Biblical writers are so gifted at exploiting traditional or standard renderings of a word or phrase that it would be a shame to always be neglecting the effects of contextual shifts because of the static image we have in our pocket that we conveniently pull out and claim to be the original or "literal" meaning.
This, then, is one of the major exegetical shortcomings of assuming that words have meanings, instead of the other way around.
If you've got more support for how this line of reasoning can be an exegetical-blunderbuss, or questions or corrections, please, lay 'em out in the comments.