In the phrase "the scales have fallen from my eyes" why did they use the word "scales"?

According to the Oxford English Dictionary, this expression comes from the Bible:

Taken (after Acts ix. 18) as a type of that which causes blindness (physical or moral).

Etymologically, it comes from "scale" in the fish sense, with the first example of "scales" being used like this coming from the 1382 Wycliffite Bible or Cursor Mundi (a1325-a1400) according to the OED. For more information, see the freely-available Middle English Dictionary.

As for what exactly is being described here, Ellicott's Commentary for English Readers on Acts 9:18 says:

The description suggests the thought that the blindness was caused by an incrustation, caused by acute inflammation, covering the pupil of the eye, or closing up the eye-lids, analogous to the "whiteness," that peeled (or scaled) off from the eyes of Tobit (Tobit 11:13). Like phenomena are mentioned by Hippocrates, and the care with which St. Luke records the fact in this instance, may be noted, with Acts 3:7; Acts 28:8, as one of the examples of the technical precision of his calling as a physician.

Elsewhere on BibleHub it says that the original word used in Acts 9:18 is "λεπίδες", which is defined as:

a scale, a scaly substance thrown off from the body.

Yes, fish or reptile scales. The expression is a standard phrase from early English translations of the Christian Bible's New Testament, and "the scales falling from one's eyes" has come to have a figurative meaning, to suddenly be able to see a situation clearly and accurately. Saul had been blind for three days, and his eyes may have covered with some kind of growths. Some scholars believe these may have been cataracts. They fell from his eyes when God healed his blindness. Some modern translations say "something like scales fell from his eyes". Of course, not everybody believes that these events ever happened.

Further to Laurel and Michael Harvey's answers, the Online Etymology Dictionary refers to scale as

"skin plates on fish or snakes," c. 1300, from Old French escale "cup, scale, shell pod, husk" (12c., Modern French écale) "scale, husk," from Frankish *skala or some other Germanic source, from Proto-Germanic *skælo "split, divide" (source also of Dutch schaal "a scale, husk," Old High German scala "shell," Gothic skalja "tile," Old English scealu "shell, husk"), from PIE root *skel- (1) "to cut."

In reference to humans, as a condition of certain skin diseases, it is attested from c. 1400. As what falls from one's eye when blindness ends (usually figurative), it echoes Acts ix:18 (Latin tanquam squamæ, Greek hosei lepides).

One can presume that Saul had scale-like incrustations on his eyes.

scales OED

4. Taken (after Acts ix. 18) as a type of that which causes blindness (physical or moral)

My sense is that it was metaphorical, in this case, as in the definition, 'moral scales about the eye'.