Learning to write a short story can really help refine your writing style. It definitely makes you think about what is important in a story and what's not. Names are often the first thing to go. Listing off five or six names all at once is not only confusing in a short story but pointless. What a reader remembers is a character type. "Oh yeah, that was the mean guy."
Another thing short stories help with is "trimming down the fat." Since you are limited in how many words you can use, this really helps you to focus on what's important in a scene and what's not. Is is really all that crucial to have a long conversation about what the characters are going to do? Or should they just go right ahead do it? This helps to improve the pacing of your longer stories.
One last thing a short story can help improve is the mood of a scene. Reactions to a scenario are just as important as the dialog. Often times one look of horror exchanged between characters can be far more telling than a wordy "I'm scared," "Me too" dialog.