1) The detailed settling of the story; 2) Constructiong detailed characters; 3) Creating in the story realistic races and creatures; 4) Establishing a culture, religion and traditions in the fantasy, and 5) Being consistent in the story.
Explanation:
The things that makes a fantasy more concrete and believable are:
1) The settling of the story, some writers rely on maps or detailed description of the area where the story is happening, in Chapter one Tolkien gives a lots of details about the location and time which the The Fellowship of the Ring is going on: “That was on Wednesday the eve of the Party. Anxiety was intense. Then Thursday, September the 22nd ”; “an enormous open-air kitchen was erected in the north corner of the field”; “They lived on the Hill itself, in Number 3 Bagshot Row just below Bag End.”.
2) Constructing detailed characters with backstory (telling about the odds, joys and dreams of their past); adding names, age and gender of the characters; defining familiar relationship between casts in the story, showing their greatness and pitfalls. Tolkien says: “There were many Bagginses and Boffins, and also many Tooks and Brandybucks; there were various Grubbs (relations of Bilbo Baggins' grandmother), and various Chubbs (connexions of his Took grandfather); and a selection of Burrowses, Bolgers, Bracegirdles, Brockhouses, Goodbodies, Hornblowers and Proudfoots.”.
3) Creating in your story realistic races and creatures, like combining features of already existing things with magical ones without going too far of already existing creatures, such as sketching humans that had a different appearance or with magical abilities. As is possible to see in The Fellowship of the Ring he mentioning the dwarf, some mythological beings that were said to have supernatural powers dealing with metals crafting: “And look at the outlandish folk that visit him: dwarves coming at night, and that old wandering conjuror, Gandalf, and all.”
4) Establishing a culture, religion and traditions in the fantasy. Tolkien talks about the habits of the hobbits and sayings: “Frodo was still in his tweens, as the hobbits called the irresponsible twenties between childhood and coming of age at thirty-three”; “but hobbits have a passion for family history”; “Bilbo's residence had got rather cluttered up with things in the course of his long life. It was a tendency of hobbitholes to get cluttered up: for which the custom of giving so many birthday-presents was largely responsible.”.
5) Being consistent in the story, this means the actions of characters, ways of living and magic tricks must follow some rule that will allow the prediction of some stuff and express some logic of how the world of the fantasy works, such as the powers of the Gandalf: “That was Gandalf's mark, of course, and the old man was Gandalf the Wizard, whose fame in the Shire was due mainly to his skill with fires, smokes, and lights”; The fireworks were by Gandalf: they were not only brought by him, but designed and made by him; and the special effects, set pieces, and flights of rockets were let off by him.".
