When someone's mortal life ends, their spirit separates and leaves behind their lifeless body. Spirits have the same visual form as mortal bodies, except that they are all in perfect adult form, even if the person died as a child. At some future point, the spirit and body of everyone who has ever died will become reunited for eternity at the Resurrection and Final Judgement, but until that day the person resides in what is known as the Spirit World.
The Spirit World is not located in some far off place. In fact, it is here on Earth, all around us. The living are surrounded by the spirits of the dead. We cannot see them because we perceive the world through a veil that prevents us from sensing spiritual things. But sometimes the veil is thin, and if Heavenly Father were to lift the veil you would see the spirit beings as plain as day.
Every spirit retains the personality, attitudes, memories, appetites, and desires for good or evil developed during mortal life. And upon entry into the spirit world, the deceased receive a partial judgement of the purity of the mortal lives they lived and their level of obedience to God. The wicked are separated from the righteous.