If someone isn't answering your calls and texts (and you haven't done or said anything unusually offensive recently), you're probably wondering if there's any way to tell if the person has their iPhone set to Do Not Disturb. It's useful for the person using the mode, but rather less enjoyable if you're the one who can't get through.
When activated on an iPhone (or iPad, for that matter), it silences all incoming notifications, calls and texts so you don't get woken up or distracted when you need to be left alone. Do Not Disturb mode was added to iOS way back in 2012, and has been a popular feature ever since.