They had tight skin with a slightly scowling expression.
The males were quite tall, often standing seven feet tall, dwarfing their Ferengi employers, and even most other Alpha Quadrant species. Despite their size, Hupyrians were a sort of gentle giant, as was seen in the case of Maihar'du, who was sobbing after the Prophets had de-evolved Grand Nagus Zek, leaving Quark to suggest that Rom "get him a handkerchief or something." (DS9: "Prophet Motive") They were also susceptible to groin injuries, as was demonstrated by Kira Nerys, who noted Maihar'du to be "Oh, so fragile," after taking him down for attempting to defend Zek. (DS9: "The Emperor's New Cloak")
They were especially popular with the Ferengi Grand Nagi, who used them as servants, food tasters, and bodyguards due to their strong devotion to service. So strong was their devotion, Hupyrian servants took a unique vow of silence which permitted them to only speak to their master (DS9: "Prophet Motive"), and for one to not show up to the funeral of their master was considered extremely unusual. (DS9: "The Nagus")
This species was pronounced as "HUE-pie-ree-an" (in the script for "Prophet Motive")
In the script of "The Nagus", Zek explained that he had faked his death using a Hupyrian sleeping trance taught to him by Maihar'du.  In the episode this was changed to a Dolbargy sleeping trance, though it was still taught by his Hupyrian servant.
The nature of the relationship between the Hupyrians and the Ferengi was unexplained, however, according to Legends of the Ferengi, by Ira Steven Behr and Robert Hewitt Wolfe, a conflict between the two species had once existed.
According to Star Trek: Star Charts ("United Federation of Planets") and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), there was a star system named Hupyria (Tau Coronae Borealis), which might possibly be the system of origin for this species, in the Alpha Quadrant. This was a binary system with a a pair of K-class stars.
In The Ferengi Rules of Acquisition, the name of the species is spelled "Huyperian".