When I think of "low" fantasy, I tend to think of it in terms of being banal vs fantastic.
Some of my favorite fantasy novels are Steven Brust's Taltos books, that feature a continent spanning empire operated in large part by the magic provided by a single hugely powerful artifact controlled by the current emperor that grants magic use to every legal citizen of the empire. It is a setting filled with magic taking place as often as high technology is used today, (but not lower, you still have the cook make the coffee in the morning, and the gardener still has a job, but if you wish to contact your friend, you communicate with him mentally via the Orb, and scorcery is as common in combat as grenades or artillery and being teleported be a professional is as normal and costly as taking a commercial jet) I consider it to be a "low" fantasy setting however. Magic is normal and the focus in the books is on the characters in an almost Raymond Chandler (The Big Sleep, Maltase Falcon) like depiction of Vlad trying to make a living, and a killing, amongst very powerful social and political forces.
"High" fantasy, for me at least, is more focused on fantastical happenings and wondrous events. It is fequently set in a low tech, low magic majority, providing the chance for "magical" things to seem more so by contrast. It is the Dream, the Fairy Tale, set just around the corner, just out of sight, but filled with wonder. I think of the King Aurther mythos, St. George and the dragon, the Trickster Monkey King, and a host of other traditional stories that made no effort to explain how "magic" worked because it was "just magic" and that was enough of an explanation.
Harry Potter falls into a strange gulf in this theory, dancing neatly between to two camps..... Hmmmm. *shrug*