What does “HC” signify in a font name?

I don’t think this has a broad or general meaning at all (unless perhaps we are strictly talking about barcode fonts). I looked into the font you mentioned, IDAutomationHC39M and here’s what I found.

• IDAutomation is the company that made this font.
• H stands for “human-readable”
• C39 is the type of code the barcode is (Code 39)
• M is the size of the font (1 cm)

As confirmation for this, I did some extra digging and found this excerpt regarding their code 39 font:

Contains 48 different Code 39 font versions for optimal compatibility
with normal, human-readable, extended and symbol versions.

(Source)

EDIT

And to address Arial HC, just about every other font with HC I find is an outline font