Taboo the word "word", and what does your question become?

A word is already partly a thing-in-the mind, and partly a thing-outside-the-mind, the latter being a sound when spoken or a string of glyphs when written. Neither the sound nor the glyphs are, or contain, meanings. If you define "word" to mean the whole arrangement, including the meanings, then you have merely answered the question by definition: meanings are contained in words. The same is true if you define "word" to mean just the sound and string of glyphs: meanings are not contained in words. This method of answering a question is incapable of being a discovery about the world.

So the question becomes "what is the relationship between the sound and the meaning?" The answer is that people learn from the speech of those around them to associate a given sound with a given meaning, and that these agreements are what enable meanings to be communicated. However, there is no necessary connection between the two, and no correlation not explained by the shared history of related languages, borrowings, and a few onomatopoeic regularities. Contemplating the meaning will not tell you the sound that people use to express it, which will be different in different languages. Contemplating the sound will not tell you the meaning, else you could understand every language without learning it.

ETA: I should also have pointed out the third thing that is a part of what can be meant by the word "word": the thing-in-the-world that people are talking about when they use the word. This book may repay study.

BTW, why are you taking a philosophy course on metaphysics?

If we put you inside a box and told you to think of a name for a cat, could we tell what the name was by looking at the cat? No, we'd have to open up the box and look at (or listen to ) you. Ditto for any similar game, like creating slang, interchanging meanings, creating private spellings, doing math and then giving names to important theorems, etc.

This only works for (at least partly-) intentional definition though - if your definition of red is to point at a stop sign, then a fire truck, then a tomato, and then to point at grass and say "not this," then we can't figure out your meaning for red just by looking at what's inside the box. First we have to get the definition from you, and then we have to go look at stop signs and fire trucks.

So depending on how you want to cash out "meaning," it can be in your mind, or in your mind+context. But it's not just in the outside world, because there's no way an alien knows what to call a capybara just from examining one.

You mean, do words have an intrinsic meaning? If that were true, there would be only one language, no? I probably misunderstood the question, but I can't think of another interpretation.

Implement a tiger-recogniser in exactly five Unicode characters and get back to us.