What is the use of Background App Refresh?
Some apps like Facebook keep getting new feed posts in the background when you are not using the app. This gives the impression when you launch the app that it is really fast and everything is already there and your main UI isn't filled with blank spots for image placeholders and things of that sort. 

The biggest impact I've seen on it is that is uses a TON of cellular data when my wife checks her Facebook on lunch break, then it keeps refreshing for the next 4 hours until she gets home to wifi. 

I try to turn off background app refresh for most apps. A good hypothetical use for it would be some app that tracks tour mileage and plots it on a map. You may be on a long trip and you don't need to be looking at a phone while driving, so this would be a good use for background app refresh so the app can continue to measure your distance even when you have your phone locked or are on the phone itself.