I think this is a pretty good summary of High Fantasy:
The core elements of High Fantasy are:
Setting – A world other than ours. It may have a nominal connection with present day Earth, such as being our remote past or future, but this plays no role in the plot. Mythopoeia is often put into play to define the very metaphysics of the world. Nevertheless it often resembles medieval Europe, and is often peopled by People of Hair Color.
Scale – Epic. Power politics, wars, the death of nations, gods walking the earth, and the real threat of The End of the World as We Know It. This is what distinguishes High Fantasy from Heroic Fantasy.
Great evil – An enemy which is near enough Evil incarnate or fundamentally abhorrent
Methods – Victory is not achieved through force of arms, the main feature distinguishing High Fantasy from Heroic Fantasy. If Aragorn had killed Sauron in hand-to-hand combat, that would have been Heroic Fantasy. In short, a Supporting Leader or the Reluctant Hero will be offered up instead of the rough-hewn barbarian of, say, Conan the Barbarian or Beowulf.
And here are some good points on Low Fantasy:
Human dominance: worlds which are populated mostly (or even exclusively) by human beings rather than the usual Tolkienesque mix of elves, dwarves and other humanoids.
Plot scope: Tends to focus more on the survival and tribulations of one or a few individuals rather than the whole world. A villainous king who steals a magical artifact is less likely to be trying to bring back the Infernal Legions of Hell and conquer the world, and more likely to be trying to make himself immortal, or conquer a few nearby kingdoms.
Heroism: High fantasy heroes are usually all-around nice guys who stand up for the little guy and fight the bad guy. Low fantasy heroes tend to be bitter cynics desperately clinging to their broken moral compass or devil-may-care anti-heroes who save the woman from the evil sorcerer just for the sex. At the very least, they tend to be closer to one of the many shades of Anti-Hero than a Knight in Shining Armor.
Methods: Victories achieved through physical combat, not magical battles or moral superiority – the defining feature of Heroic Fantasy.