According to a periodic table shown during a Next Generation episode, it has the atomic number 87 (which in reality belongs to francium), and the chemical symbol Dt.
The fictional properties of the material in the authors' guide Star Trek: The Next Generation Technical Manual (1991) explain it as uniquely suited to contain and regulate the annihilation reaction of matter and antimatter in a starship's warp core: In a high-frequency electromagnetic field, eddy currents are induced in the dilithium crystal structure, which keep charged particles away from the crystal lattice.
Hence story lines based on the need for natural dilithium crystals for interstellar travel – much like real-world equivalents such as oil – made deposits of this material a highly contested resource between fictional factions in the stories, and as such, dilithium crystals have been used by writers to introduce interstellar conflict more than all other reasons combined.
The annihilation reaction heats the excess deuterium gas, which produces plasma for the nacelles and allows faster than light travel.
In addition, film sets representing the crawl-spaces for the inner workings of starships tend to be depicted as adjacent to the "EPS" conduits that channel plasma to critical ships' internal systems.