Vessels and nerves of the choroid and iris
This cutaway diagram clearly shows the position and relation of the sclera to the inner workings of the eyeball.
Comprising the posterior five-sixths of the connective tissue surrounding the eyeball, the sclera is contiguous with the cornea (the anterior one-sixth of the connective tissue) and the dura mater surrounding the optic nerve. Yes, that’s the same “dura mater” connective tissue that’s found surrounding the brain - in mammals, the eyes are simply outgrowths of the brain itself, not independently developed sensory organs (as they are in, say, cephalopods).
Also known as “the whites of the eye”, the sclera is comprised primarily of collagen and elastic tissue, and is a fairly durable and tough outer casing for the inner structures of the eyeball. Directly interior to the sclera is the choroid, which provides much of the structural definition and vasculature of the eyeball, but is very delicate on its own.
Humans are fairly unique among mammals in that the whites of our eyes are always showing. The small size of our irises and the contrast against the sclera allows us to clearly communicate nonverbal (and often subconscious) cues to one another using only our eyes.
Anatomy: Descriptive and Applied. Henry Gray, 1910.