The primary reason I believed Tolkien's books was not because of the compelling reality of his writing, which is not always as marvellous as his imagination, but because of his philology. In his world, as befits an expert on Anglo-Saxon and Middle English, the languages cohere: they are not random, but obey linguistic laws which sees the etymology of words and names changing with times and usages, and in which each different language has its own grammar and diction and script. Another reason I believed him was his detailed descriptions of the natural world, which I suspect derived from endless walks about the various regions of England and his deep love of the countryside. The reality in the books emanates from the realities Tolkien valued.
There are many ways of making a fantastic world seem real, and I suspect they will always reflect the particular interests of the writer. Despite his ability to make appealing characters if he wished, Tolkien was scornful of character-driven narrative, believing it to be a corruption of fairy story that stemmed from drama; an issue on which I deeply disagree with him. In the end, the only necessity in writing a fantasy is that it is compels belief, and there are many ways of achieving that. I'll talk briefly about the aspects on which I concentrated in my own books.
An important part of reality is its physical manifestations, especially its geography. That leads to the great fetish of fantasy writers: The Map. Like many teenagers, I loved making maps, and writing these books has permitted me to return to that childhood enthusiasm. My father was a geologist, and I spent much of my childhood learning to perceive a landscape not as, say, a collection of pretty hills surrounded by a plain, but as the evidence of volcanic activity millions of years before. However superficially, a map had to satisfy my ideas of being credible in order to satisfy my own sense of reality. For me, a credible map adds much to the reality of a story: it is a way of creating a landscape with a history, just as philology creates a language with a history.