I think Henry is right in that there seems to be a fairly wide spectrum of ideas on what exactly "low" means in this context.
If "Low Fantasy" is the sense that Low = "Base", I would say then it's being compared to a "High" that ="Epic" or "Heroic." Protagonists are larger than life. Blessed by gods, chosen ones, etc. "High Fantasy" adventures in this context are things like save the world, win the kingdom, etc. "Base" fantasy would be where the characters are less special or heroic. The world hasn't been awaiting their birth for centuries, they aren't all that much tougher (initially) than the people around them, etc. The setting can be highly magical, bizarre, alien, etc. but the "heroes" have no special place in it. "Gritty" is a term often associated with this kind of world. Though it isn't a requirement.
If "Low" fantasy = "Less" fantastic. Then you're talking about a world that is more mundane, possibly less magical. Less magic might mean there is very little if any magic in the world, or it might mean that it's very rare, but can occur in very powerful and mysterious forms.
To my mind, a world like WHFRP's "Old World" is Low Fantasy in the first sense. It is gritty and dark and grim. The characters struggle to survive to a degree. While the characters may act nobly, the world isn't really set up to accomodate "heroes" in the whole Great Destiny sense. Not all "Base" fantasy settings are dark and grim, but it's pretty common. Magic is all around in the Old World; everyone knows there are wizards and gods and monsters. Many people fear them and hate them, but they know they exist. It's not Low magic, it's a world where magic isn't widely accepted.
At the other end of this scale might be a world like Middle Earth. Magic is subtle, but exists. While it's true what Henry says about how unusual magic items are, magic itself is fairly easy to find and is readily accepted as real. Bilbo gives away magical dwarven toys at his 111th birthday. Dwarf-doors are sealed with spells. Old Man Willow shifts the paths of the Old Forest to lure unwary travelers. Giant Spiders, Goblins, Ents, Trolls, etc. Magic/fantasy is everywhere in Middle Earth. The protagonists of these stories are heroic and noble, not only in the manner but in the sense that they have destinies to fulfill and are less concerned with mundane issues (the don't loot the dead orcs and sell the gear in town, etc.

). There are forces of fate and destiny at work in their lives and they fight for the forces of GOOD against absolute EVIL. Very epic, very heroic. There aren't
+5 Flaming Holy Avengers, Cure Critical Wound spells and magic users don't lob fireballs, but it's a very magical world.
For the second kind of "Low Fantasy," the world would be a place much like ours in the sense that very little wouldn't be "normal." Magic would have no place in day-to-day living. Magic items, spells, monsters. These things are legendary, but not to be believed in or counted upon. Many people might live their whole life without seeing a single example of magic.
A High -or "Heavy"- Fantasy world in this sense is one where magic/fantasy is completely integrated into the daily life. Most classic D&D settings fit this bill: Elves & Dwarves wandering around town, entire races of dragons, magic swords & healing potions for sale, wizard colleges, etc. etc.
It is possible to combine these elements in different combinations:
A "Base-Heavy" world might be a world like WHFRP
A "Heroic-Low" world could be Middle Earth
A "Heroic-Heavy" setting? Perhaps Forgotten Realms (though how "heroic" the PCs act and their adventures are can vary

)
A "Base-Low" world? hmmm. Perhaps the old Conans? I'm not that familiar with those stories, though, so I could be wrong on that one.