It's a simple request, but it can be used in different contexts, for example:
* Games: In word games, someone might ask you to "state a word" that fits a certain category or rule.
* Tests: A test might ask you to "state a word" that has a specific meaning or is related to a given topic.
* General conversation: Someone might ask you to "state a word" if they need you to provide a specific term or name.
The important thing is that the person wants you to say a single word.