It can be said at the outset that Burroughs was not a very deep nor a very disciplined writer. His disdain for research often shows in his work, and it does here; and in his science fiction (he would write voluminously in this genre --this novel sparked a series, and he produced two other popular sci-fi series as well) consistent and well-thought world building wasn't his strength. For instance, his Martian children incubate in eggs and hatch only when they're able to eat solid food --but his Martian women have physiques like those of human women, busts and all. If there were ever a writer who overused coincidence in plotting, it would be Burroughs, and his plot developments and devices can strain credibility; science fiction writers of that day were quite taken with astral projection, but John Carter's ability to, in effect, simply will himself to the Red Planet, as a means of space travel, is definitely a stretch.
For all that, though, his work continues to fascinate readers. Partly, this is because of the enduring appeal of his theme of "primitivism" or "feralism," of which Tarzan, of course, is the archetypal example, but which constantly reappears in his work: the saga of a scion of modern high- tech, regimented civilization, transported to a primitive, dangerous world where he can be free to be his own boss, but must meet physical challenges in order to survive. And his heroes earn our respect, because they're not egoistic brutes who revel in a chance to be predators in a jungle; rather, John Carter and the others are instinctively moral men who model what Burrough's generation thought of as "masculine virtues" (which actually aren't gender-specific!) --courage, loyalty, a sense of honor, determination, generosity of spirit. (Of course, they're also larger-than-life heroes with strength, ingenuity, and competence.) This gives his work a dimension of meaning, both as an implicit criticism of a stultifying and constraining social order that tries to reduce us to cogs in a constantly smooth-running machine and as a positive endorsement of qualities we recognize as worth honoring and imitating, that still resonates with readers today, and I think always will. He's also a master of pacing, and of exciting adventure that can keep you turning the pages; and the broad canvas of his picture of Mars --an arid, dying world balkanized among a plethora of warring tribes and kingdoms, violently struggling for survival-- has an undeniable imaginative power that grips the reader.