It can look nice. It sets the photo apart from everything else around it, just like putting a photo in a nice picture frame.
Also, it sometimes alleviates the problem of posting multiple images of different sizes. Instagram likes to make all images conform to the ration of the first image chosen. If you put a border around images, you can adjust the size of the photo with the border to keep images consistent.
Flickr is one of the few places where I feel like photos are posted as photos for people to enjoy, and not just to get likes. Some people have amazing looking galleries on there.