Greetings,
Appropriacy in language use at its basic level is to do with how we should use language in different situations. To begin thinking about this, consider how the words you say would be different if you were talking to your best friend or if you were talking to the King or Queen (or President, etc.) of your country.
What would be different?
Well, your
vocabulary would probably differ. That is, you would use different words. For example, you might use slang terms with your friend, but you would be unlikely to do this in front of a very important person - instead you would probably try to speak formally and correctly. You might have words that only you and your friend know the meaning of, like a private joke. You would obviously not use words like that in front of the VIP.
Your
pronunciation might be different. Again, you would be likely to use a more casual tone of voice with your friend, whereas in front of the VIP you might make an effort to speak very clearly and precisely.
There are other ways your use of language could differ, too, and they are all being referred to when someone talks about appropriacy of language use.
Other situations where appropriacy could be an issue:
What is appropriate language in a business meeting may be different from appropriate language in a religious service.
Appropriate language on a sports field will be different from appropriate language inside an operating theatre.
Keep in mind, though, that we are talking about something
other than the specific jargon (or lexis) used in these different areas. Whether to use the word "glossopharyngeal" or not will usually depend on whether or not you are in a medical situation, and this is a slightly separate issue from appropriacy.
Here is a page showing a lesson plan for teachers of English as a foreign language covering this topic.
Here is a very useful overview of the different aspects of language that can be covered under the heading of "Appropriacy". Note that this author
does include jargon, whereas I think it's slightly different. That's not a hugely important difference, and it shouldn't stop you from understanding the concept.
I hope that's been helpful - let me know if there's anything else you need.
Peace