Have you ever heard your teacher say "class, quiet please" or "students, listen up"? The word "class" and "students" in these sentences are examples of the essive-formal case.
The essive-formal case is a grammatical term that we use to show that something or someone is acting in a formal or official capacity. This means that the word is used to describe a role or status that someone or something has, rather than just as a regular noun.
For example, let's say your friend Bob is hosting a fancy dinner party. He might introduce himself to his guests by saying "welcome, I am your host for the evening". In this sentence, "host" is in the essive-formal case because it is describing Bob's formal role as the person in charge of the party.
Similarly, if you are in a court room and the judge says "Counsel, approach the bench", the word "counsel" is in the essive-formal case because it is describing the formal role of the lawyers who are there to represent their clients.
In short, the essive-formal case is a way of showing that a noun is being used to describe someone or something's formal or official role or status. It's a bit like wearing a special hat or uniform that shows everyone that you have a certain job or responsibility.