Use this informal word when you want to emphasize a large but vague quantity. If you get umpteen text messages from your friend reminding you to return the sweatshirt you borrowed, you know she really wants it back.
Use umpteen when you have so many of something that it's not even worth counting them. It's kind of like saying "a zillion." If the smell of your dirty gym clothes is wafting into the hallway, your parents might complain, "We have told you umpteen times to clean up your room!" Umpteen started as World War I Army slang, from umpty which means either "of an indefinite number" or "dash" in Morse code.