Our tendency to find faces in inanimate objects is due to a neurological phenomenon called pareidolia. The cause isn't totally clear, but it's probably an evolutionary quirk: Humans are adapted to be really, really good at recognizing human faces as other humans, even when they're new to us or the lighting isn't great. It could be that our brains jump the gun a little and find pseudo facial features where we know there aren't any, leading us to have the unsettling-but-amusing sense that our electric sockets are gaping at us.
In this case, the cosmic "face" is actually caused by a neat galactic phenomenon as well: gravitational lensing. Large galaxy clusters sometimes produce such a strong gravitational pull that they warp the time and space around them. This can be a great thing for scientists on Earth, because that warping can act as a natural "lens" and magnify faraway objects behind the clusters, making them more visible to space telescopes. But the magnification also warps the objects.
The ring that makes up the "face" is called an Einstein Ring, and it's produced by a very particular view of one such warped galactic cluster. Another line of warping forms a lopsided smile.
Inside the ring, two bright galaxies are perfectly positioned as eyes, completing the illusion.