Looking on my phone, it’s a fairly horizontal image that shows up when you view a user (in either the popup when you click their name, or when you go to the profile). With my phone on portrait orientation, the horizontal width goes across my whole screen and the vertical height is about the width of a large thumb.

Examples of banner pictures I’ve seen include nature, people, animals, nsfw content, and memes. The picture can really be anything. Again, people will only see the image if they click on your name and/or go to your profile.

Basically, it is a landscape, rectangular image at the top of your profile. It's quite big, and is one of the first things someone sees when they click on your profile. It's just like a profile picture really, just rectangular and a bit bigger.
You don't have to set one, a lot of people don't. People set all sorts of things, like a profile picture. It could be a picture of you, you and your family, just a sunset, anything. Mine is set to a graphic which just has my name written on it with a blue background and white text.
Hope that helps!