A short story is a type of prose fiction.
Prose simply means it is written in sentences and paragraphs, and is not a poem or play script.
Fiction means the story is made up, though of course you can base your story on something that has really happened.
A short story is not a cut-down novel. In a novel the author has time to develop characters and show us many events in their lives. A short story takes characters at an important point in their lives and gives us a snapshot of a significant moment.
The best way to understand what is required in short story writing is to read short stories by different authors. There are many good anthologies of short stories available in libraries or bookshops. Ask for a recommendation if you are not sure where to start.
There are no rules with short story writing but this guide contains some suggestions that should help most people to improve their writing.