How is context "king" in deriving meaning from words?
I think it just derives from the belief, common both among Biblical interpreters and linguists, that all meaning is contextual.
Some dictionaries make it seem like words just have meanings in isolation from the rest of the language. Better dictionaries show how words relate to each other, how they're used and connected with each other. It's especially important with polysemy to understand that although the same sequence of sounds or letters may have many different meanings, it is almost never the case that all meanings are possible in a given utterance. You cannot ignore context and hope to have any understanding of a language.
It also reflects how our brains process language: our brains do not need to be fed in meanings of new words before we can use them. Instead, when we come across a new word, our brains will automatically start working out the meaning based on the context we see it in, often without us really being conscious of this process. As we see the word in more contexts we refine our understanding of what it means.
Context is king also seems to be taken up due to the way we communicate and interact. We now often have very short interactions with people and more and more this happens through the computer, so we cannot see what context the sender is in.
Some typical examples
- Tweets! Human communications don't get much more compact than this. These days even something like 'time for chicken' could probably be interpreted in so many different ways that context such as who is saying it, in what setting, and with what history of their previous messages or topics, to get any idea of which meaning to assign.
- Searches Nowadays people find things by typing a minimal amount of words into a search engine. This means that context (such as where/who/when you are, or what you did) becomes at least as important as the terms that you use in most cases. This applies to anyone who wants to act on searches, for instance search engines and marketing teams.
In short, we live in a world where context is no longer passively available and communications are compressed. It is therefore very important to have context to interpret the meaning of anything.
Depending on your circles, of course the more classical field of translations may also be a relevant field. This was already covered adequately in the existing answer.
Based on your compact question and without me looking at your history or profile, you may be looking for either of these. Hence, using circular reasoning towards my own initial interpretation I declare this to be a prime example where Context is King.