> had no idea what was meant by "context" as it's a highly ambiguous word and is never mentioned with any concrete definition

(forgive me if you know this and are asking a different question, but:)

I don't know how familiar you are with LLMs, but "context" used in that context generally has the pretty clear meaning of "the blob of text you give in between (the text of) the system prompt and (the text of) the user prompt"[1], which acts as context for the user's request (hence the name). Very often this is the conversation history in chatbot-style LLMs, but it can include stuff like the content of text files you're working with, or search/function results.

[1] If you want to be pedantic, technically each instance of "text" should say "tokens" there, and the maximum "context" length includes the length of both prompts.