LDS definition: The highest of the three degrees or kingdoms of glory in heaven, where one is in the presence of Heavenly Father and Jesus Christ. The glory of the celestial kingdom is compared to the glory of the sun in the scriptures.
Interestingly, Joseph Smith is often credited with being the first person to claim that there are three degrees of glory (which no one can prove or disprove is really the case). But this concept has also been around a long time. In 1784, Emanuel Swedenborg wrote a book called Heaven and Hell and Its Wonders about his visions of the afterlife. Swedenborg insisted: "There are three heavens," described as "entirely distinct from each other." He called the highest heaven "the Celestial Kingdom," and stated that the inhabitants of the three heavens corresponded to the "sun, moon and stars."