Things that are nonstop keep going all the time without pausing. A week of nonstop rain can cause flooding, and be pretty gloomy too.
You can use the word nonstop as an adjective or adverb, and while it can literally mean "without stopping," it's also frequently used in an exaggerated way, to mean "a lot of the time." Your friend's description of a nonstop dance party or a nervous substitute teacher who giggles nonstop are examples of this. A nonstop plane flight, on the other hand, literally flies from one city to another without landing at another airport on the way.