Thanks!
Hard fantasy has a rational, plausible system of rules for the setting, which includes the definition and use of magic. The system used does not bend for a narrative, "hand-waveum" convenience. That doesn't mean that hard magic has a scientific explanation and current logical principles; rather it has an internal consistency.
Hard fantasy doesn't necessarily mean low fantasy and not just about magic, but does take into account magical principals on everyday society. Since we're on the RPG site and not the special snowflake site, let's use gender relationship dynamics as an example--if we say in a setting where divine, elemental magic has an equal chance to appear in either a male or female, that impacts how a feudal-like society treats women. You have more than physical strength to bring to the table in many prominent roles, such as serving the common folk and waging war.
However, what if humans evolved from their current state and then someone like the asshole elves (but I repeat myself) introduced them to magic? Well, that's tension and somewhere in history, societal upheaval.
What do the gods feel about birth control? If there are real gods that derive power from mortals worshiping them, and in a hard fantasy setting, power at risk for not having enough of it, what's the role of a pregnant woman with sorcerous power? What is she allowed to do, and who enforces the rules?
The list goes on-and-on. How long would it take society with access to divination magic to stop throwing poop in the streets, and people should wash your hands before dinner? If there is a druid with minor healing magic in every village, what does that do to infant mortality? Would death from childbirth complications even be a thing?
I love hard fantasy. We might not get it right all the time, but you can see the principals at work in our premier mega-module, and the players love it. Hard fantasy takes things like "finding the secrets of the abandoned temple" and puts a fresh spin.
Thus endeth my screed on hard fantasy, heh.