First, in order to understand what happens when we die, we have to understand what happens when we're born. Each individual has always existed, and always will, but before this life, was a spirit, and before that, an formless intelligence. In the pre-existence (perhaps more accurately referred to as the pre-life, as opposed to after-life) there was a war, not physical, but a war of ideology. Of course, Satan and his followers lost and were banished to the outside... here, without body. Those that remained valiant, about 2/3 of the hosts of heaven, receive or received bodies, our second estate.
That war will be discussed in further detail later.
So, anyway, we came here, as a sort of test, and receive bodies, and after we die, our spirits leave our bodies and enter the spirit world, which is divided into spirit prison (commonly known as hell, but it isn't the end), and spiritual paradise. Which one a person enters depends on how he or she lived in this life. We remain there until resurrection, which, really, could happen at any time, but the large majority will have to wait until the Millennium. After the Millennium, we have final judgement, and, based on how we've lived and if we've repented, we can enter one of three kingdoms of glory. The lowest, the telestial, is reserved for the most wicked, and it is far greater and more glorious than we can imagine in this life, such that if you were to see it in your mortal state, it would probably kill you from shock. The second, the terrestrial, is more amazing than that. The highest, the celestial, is for only those who were most valiant and repentant. Unless one enters the celestial, progression comes to an end, and that's it. Those who enter the highest degree of the celestial kingdom receive exaltation, and become as God.