Why your eyes are horizontal not vertical - the laundry line explanation.
When I was in the Peace Corps in Lesotho in 1990 I did my laundry by hand. I would carry my clothes in a plastic wash basin about 1/4 mile down to a stream. There, along with my students and other folks who lived in the nearby villages, we would engage in a recurring ritual of washing, wringing and polluting the local water supply. Good times.
After our clothes had been partially dissolved by Omo, the local detergent, and we had dirtied the water supply of all the downstream villages, we would carry our much heavier wet clothes back up the hill and hang them on laundry lines.
Being a teacher and someone of modest respect, I had my own laundry line that I only shared with a local nurse.
I did this ritual once every week as did nearly everyone in Lesotho.
My friend and fellow Peace Corps Volunteer Tim Meisburger commented once that seeing a thin laundry line (often a piece of metal wire strung between two posts) with your head steady and the line stretched taut, was quite difficult. Your eyes often couldn’t focus on the wire. Your depth perception would put the wire either too near or too far away. Usually, your head was moving enough so that you didn’t notice this problem. But we’ve all had the moment where an object that is small or difficult to see is suddenly misplaced in our vision and our brain’s visual cortex mistakenly places it too far away or too near. A blink or a head movement will cure the issue.
The laundry line issue comes about because when your head is upright and your eyes are horizontal and thus parallel to the laundry line, the angle of each eye to the laundry line is the same. With no difference in angle, your brain cannot infer a distance.
Depth perception is possible for humans because we have more than one eye. Binocular vision allows for depth perception because the angle of an object to each eye is slightly different and our brain calculates the distance. 3D movies work because the glasses you wear separate the movie into two separate images. The different image in each eye allows our brains to infer a distance to the objects displayed on the movie screen.
And this is also why if you lose the sight in one eye you also lose much of your depth perception, though head movement will allow your mind to calculate depth because your single eye will see objects from different angles over time rather than having two eyes seeing an object from different angle simultaneously.

Interestingly, as Tim pointed out, one solution to properly focus on the laundry line and see the proper distance of the line is to turn your head sideways so that your eyes are vertically aligned instead of horizontal. In this way, the angle of each eye to the wire is different and your brain can properly infer (or perceive) the distance of the wire to your eye.
THE WEIRD STUFF
So, WTF?
Let’s consider the following question. Why aren’t our eyes vertically aligned? Or why are our eyes horizontally aligned?
For example, here’s a kid:

Why aren’t his eyes like this?

Seriously, isn’t that the same? Aren’t two eyes vertically aligned the same as two eyes horizontally aligned?
What about these creatures? Why don’t they exist?

[So this is my theory, which is mine.]
In fact, nearly all terrestrial creatures have horizontally aligned eyes. And the reason is that most objects in our world are vertically aligned (perpendicular to the ground).
Trees, other people, mountains, etc. are vertical, parallel to gravity. And evolution has given us the most efficient sight system to see the world around us.
In fact, most objects are perpendicular to the ground - they are parallel to gravity.
But this begs the question, why are our eyes horizontal? Why not at some other angle?

Or why not many eyes?

And the answer is biological efficiency. Why don’t we have two hearts? Or sixteen lungs or some other number? In fact, evolution and natural selection or God or Bob The Creator or whatever you want to call it, has caused us to interact with our environment in the most biologically efficient manner. Building and maintaining a brain to process information from more than 2 eyes would be more biologically expensive than building a brain for 2 eyes.
Many insects have more than 2 eyes. Why? Perhaps they regularly interact with their environment in a way that is not parallel to gravity. They fly, they have landed on surfaces that are not horizontal to the ground or they are moving in ways that cause their vision to be not horizontal to the ground. And so they need to be able to process visually in a way that allows for non-horizontal sight. Hence, more than 2 eyes.
Of course, this doesn’t answer the question of why and how 3 eyed people didn’t evolve?
And my answer is that three eyed people would be better equipped to live in a world without gravity, where objects existed normally in a plane that is not parallel to gravity, but instead existed at random angles to the viewer. In that case, horizontally-based binocular vision would not be the most effective way to see the world around us.
If you want to see how difficult it is to operate with your eyes vertical, go ahead and try to pick out objects when you are lying down. You’ll find that your depth perception is different. This is not to say you don’t have it, but your mind doesn’t perceive depth as well sideways as it does when you are upright.
Let me add that I didn’t do a lot of research on this topic except what you’ve read here. I’m sure there are scientists who know all about this who will explain this better with more diagrams and better credentials. To them I say, Hi, can I have a beer?