The Dwarf, who is never given a name in the book, is one of the few servants of the White Witch who is "onstage" a lot in the course of the novel. The Dwarf drives the Witch's sledge and carries out her evil errands. He seems to take pleasure in her cruelty, especially toward Edmund.
However, unlike a regular servant, the Dwarf seems to feel comfortable arguing with the Witch and sometimes talking back to her. When the magical winter in Narnia dissolves into spring, the Dwarf is brave enough to tell the Witch that Aslan must be taking charge and that her power is waning. The Witch also seems to value the Dwarf more than she values the other evil creatures that serve her; when they are ambushed by some of Aslan's people, she hides the Dwarf as well as herself using her magic.
Dwarves are interesting in Lewis' Narnia books because they're one of the only creatures on both sides of the war between good and evil. In most cases, a creature's nature seems to determine whether it follows Aslan and everything that's Good, or whether it follows the Witch and everything that's Evil. For example, hags, wolves, and ogres are all inherently evil (apparently), while dryads, unicorns, and lions are inherently good.
However, some creatures are able to make their own choices; there are dwarves on both sides of the battle. (Trees, giants, and human beings are some of the other creatures that are divided between Good and Evil.) It's important not to confuse the Dwarf who serves the Witch with any of these other dwarves who show up here and there in the book. When we discuss The Lion, the Witch, and the Wardrobe, we'll call this dwarf "the Dwarf" or "the Witch's Dwarf," and we'll call any other dwarf "another dwarf."