Source of the material is: http://ritchieslatin.blogspot.com/2011_03_20_archive.html
- Think "brazen", and the idea of Medusa's hands as deadly weapon.
This is a fairly common metaphor in heroic literature, and I've come across it in English language heroic literature and English translations of heroic literature, typically used for the double meaning. Brazen here is defined as "hardened effrontery", in the sense of transgression, thus something that can pierce or penetrate established boundaries, such as the skin of an adversary.
Weapons and armor were made of bronze, thus the "bronze age", such that it connotes something hard and potentially deadly.
Milton uses this in Paradise Lost: "The Serpent suttl'st Beast of all the field, / Of huge extent somtimes, with brazen Eyes / And hairie Main terrific." (7.495‐97)
Here it might be blazing (usage of words related to bronze in many languages meant to convey brightness.) The association of bronze with weapons draws a distinction with the other bright metals, gold and silver.
Another usage is Leviticus 26:19: "And I will break the pride of your power, and your heaven that is over your head shall be bronze, and the earth that is under you shall be iron."
Here the usage is clearly meant to convey unyielding. So too can Medusa's hands be assumed to be.
A direct reference to use of bronze in reference to body parts (here eyes) may be from Homer: οὐρανὸς χάλκεος, πολύχαλκος, ὄπα χάλκεον. [OED, unsourced]
Although the source material is unreferenced, Graves translates as "brazen claws" [The Greek Myths, 33.b], thus one may interpret that it is not the hands, specifically, but sharp fingernails or literal claws, per Medusa's metamorphosis.
A note on aes: It connotes any "base" mental (i.e. not silver or gold), and can mean iron. The Lewis lexical entry further elucidates: "ex aere statua — As symbol of indomitable courage."
Usage in literature supports the idea of "brazen" per bronze, and Apollodorus specifically uses the term χάλκεος.