To understand the connection, remember that owls are nocturnal birds: they hunt for food at twilight and even in the dark. Food for an owl may be something as large as a rabbit or as small and hard to see as a field mouse. Not only is this kind of meal difficult to spot, it also has a tendency to bolt away quickly at the slightest sound.
The owl overcomes these difficulties by having evolved a visual system that works even at great distances and in low light. This is partly the result of having large eyes that are set on a relatively flat face, thus increasing binocular vision. However, those big eyes don't move much in their sockets, and the owl's total visual field is therefore reduced. At any given time, it only sees about one third as much as birds with eyes on either side of their heads.
That means the only thing to do is to be able to turn those staring eyes in any direction, without the noise that would be caused by actually getting up and moving. And now you can see how the staring eyes and swiveling neck work together: the owl's super-flexible spine allows it to remain silent while it scans 180 degrees on either side. Yes indeed -- from a forward-facing position, an owl can look entirely backwards.