I use the term "pulp fantasy" a lot when talking about the history of Dungeons & Dragons and my own particular take on the game. So far as I know, it's not a commonly accepted term and, even if it were, I use the term somewhat idiosyncratically to mean roughly "whatever stories influenced Gygax and Arneson when writing OD&D." Now, I do have a more precise meaning that, because, for example, even though Tolkien was an influence, if a distant one (at least on Gygax, since Arneson, so far as I know, has always acknowledged the Professor as a major influence on Blackmoor, a fact confirmed by his former players on more than one occasion), I don't include his works under the "pulp fantasy" rubric, as they clearly don't belong there. So, what is pulp fantasy and what do I use that term?
In general, "pulp fantasy" roughly equates to what we nowadays call "sword and sorcery." However, the term is more expansive than that, because it also includes authors and stories that do not, strictly speaking, fall under sword and sorcery, such as Burroughs and other "sword and planet" authors, as well as "weird tales" of the Lovecraftian variety. I chose the term because, by and large, most of the authors whom Gygax cites as influences in the famous Appendix N of the AD&D Dungeon Masters Guide were published in the pulp magazines of the 20s through 50s. There are exceptions, of course, such as Jack Vance, whose "Dying Earth" books (the first of which was published in 1950 and the second in 1966) were hugely influential of D&D, so much so that the game's peculiar form of spellcasting is termed "Vancian" because of its vague relationship to the magic of Vance's far future fantasies.
By and large, "pulp fantasy" stories are those written before 1970 and the adventure of what we now consider fantasy literature. They have a very different cast to them than Tolkien or his legions of imitators. Firstly, these stories feature characters that are, by many standards, morally ambiguous. While rarely outright villainous (though there are exceptions), few are what could be called "heroes" without qualification. To put it another way, pulp fantasy protagonists are very human, full of foibles and flaws that lend a kind of rough verisimilitude to their adventures. Such characters are motivated at least in part by the quest for wealth and power -- just as D&D characters clearly are. That's not all these characters are about, but it's an important component to them. Likewise, pulp fantasies are very character-centric. That is, the threats these characters face are usually quite personal or, at least, possess an immediacy for the character without too much emphasis on the wider world. Pulp fantasies rarely have Sauron wannabe "dark lords" in them except insofar as such antagonists stand in the way of a pulp fantasy character's achieving wealth, power, or the company of a beautiful woman.
Another element of many -- though not all -- pulp fantasies are their lack of naturalism. This is just a fancy way of saying that they're fantasies. You won't find a lot of scientific plausibility to the monsters of pulp fantasy stories. There is no "Ecology of the Deodand" and understandably so. The threats of such tales are not just personal ones, but they exist primarily to drive the particular story the author is telling rather than being part of some grand exercise in world building. Pulp fantasy settings, such as they are, mostly exist as vehicles for stories rather than the other way around. This carries over into early D&D, where settings arose organically through play rather than by design beforehand.
This is what I mean by "pulp fantasy." It is these things that gave rise to OD&D and most of its mechanical and conceptual elements. It is also these things from which D&D has been slowly fleeing for the last 20 or more years of its existence and why I believe the game is need of a restoration.