One of the best things about the Church of Jesus Christ of Latter-Day Saints is the Plan of Salvation. It is awesome! No other Christian church can tell you where we've been, why we're here, where we're going, and why we're trying to get there. The Plan of Salvation is so wonderful to know, because it really puts things in perspective. Here, I'll explain it. First, let's look at a diagram:

The Premortal Existence
Yes, we existed before we were born! We didn't just pop in out of nowhere - our spirits have been around for a long time. In fact, we're older than the earth itself. We were all gathered together in the premortal existence in a grand council. There God appointed some to be rulers¹, and the Plan of Salvation was introduced. God's plan was to send us to earth to be tried and give us a Savior to save us from the sins we may commit. Although not every soul would make it back to Him in the end, those that did had grown during their time on Earth. An angel named Lucifer also had a plan. He suggested a plan that would have made sure everyone got back to heaven, but no one would have free agency². We'd all be little robots doing the same thing, and we wouldn't learn anything at all. Lucifer also wanted the honor and glory for this plan³. Heavenly Father decided on the first plan. This made Lucifer really upset, and so he rebelled. One third of all the spirits in heaven sided with Lucifer.⁴ There was a big battle, and Lucifer and his followers were cast out of heaven.⁵ This is how Lucifer became Satan.
So see, we already started out on the good side! We all sided with Heavenly Father in the premortal existence. How do we know that? Well, Abraham 3:26 says that only those who keep their first estate will be added upon, meaning that only those who sided with Heavenly Father in the premortal existence would get to come to Earth. And what's more, we're some of the choicest spirits. President Ezra Taft Benson teaches us that "For nearly six thousand years, God has held you in reserve to make your appearence in the final days before the coming of the Lord....God has saved for the final inning some of His strongest children, who will help bear off the kingdom triumphantly."⁶ Isn't that neat? We were some of the coolest spirits up there!

The Mortal Existence
So we were sent down here because we were so good, after we had a veil put over our minds so we don't remember what happened in the premortal existence. Be happy - this is our reward for being good! Which is why there is so much crime and hurt and everything...Huh? That doesn't make sense! This can't be a reward, right?
Okay, so why exactly did we come down here? Well, there are several reasons. The first is to be tested. It's easy to say how much we love Heavenly Father if we're sitting right next to Him. It's a whole lot harder if you never see Him and seldom hear his voice. It's easy to forget Him. Abraham 3:25 specifically says we're put here to be tested, and Abraham 3:26 adds that if we pass the test, we shall be exalted. This leads me to my next point. We are here upon the earth to learn and progress and become more like our Heavenly Father. All our trials are here for our experience⁷, and Heavenly Father will never allow us to be tried more than we can handle⁸. He wants us to progress towards immortality, and is working to help us do so. In Moses 1:39, He states, "Behold, this is my work and my glory: to bring to pass the immortality and eternal life of man."
Another reason is so we can be happy⁹! Heavenly Father is a loving God -- he didn't just toss us all down here so we could be miserable. That would be awful! No, he wants us to be happy, and we will be happy if we follow His word. Finally, we're here so we can get a body. Remember the premortal existence and how a third of all the spirits were cast out with Satan? Well, they don't get bodies, which means they can't really do too much. Have you ever thought about what it would be like to not have a body? Think about that next time you're looking in the mirror and you're thinking your body is ugly; be grateful that you actually have a body.

The Post-mortal Existence
Okay, you're reading this page and all of a sudden, a bolt of lightning strikes you dead! What do you do? Well, okay, that was a silly question. You can't do too much because you're dead. A better question would be, "What should you expect?" Well, right after we die, there are two places we can go, based on how we were in life and if we took Jesus as our Savior. That's what everyone believes, right? Well, there's more! (Dun dun dun!) Heaven and its opposite, the spirit prison are just temporary abodes. We're not meant to stay there for all eternity; we're only there until the Resurrection. Then everybody gets resurrected, except for those who were evil people who denied Christ and the Holy Spirit after having felt them. They are the only ones who will not be resurrected¹⁰. Then the Savior Himself is going to judge us according to our deeds¹¹.After that, we go onto one of three kingdoms¹².
The first kingdom is the telestial kingdom¹³. It is where people go who weren't really that great of people but still believed in the Holy Ghost and all. Even though it's the lowest kingdom, its glory still "surpasses all understanding" (D&C 76:89), so it's not that bad of a deal. The telestial kingdom has been compared to the stars in glory¹⁴.

The next level is the terrestrial kingdom¹⁵. This one is even better than the previous one. The people here were good in life, but they didn't get baptized for some reason, or maybe they did get baptized but weren't really valiant in their testimonies¹⁶. They get "the presence of the Son" with them, but not the Father¹⁷. The glory of the terrestrial kingdom is even better, "which excels in all things the glory of the telestial, even in glory, and in power, and in might, and in dominion" (D&C 76:91). Where the telestial kingdom is like the stars, the terrestrial kingdom is like the moon¹⁸.

The highest and best kingdom is the celestial kingdom. In order to get into it, you have to be valiant in your testimony - doing the Lord's will because you really want to, not because you think it's something that maybe you ought to do. Also, you need to get married¹⁹. Other people who get into the celestial kingdom are people who died without hearing the gospel, but would have accepted it wholeheartedly²⁰, and little children who die before they're 8 years old²¹. The Father resides in this kingdom²². It has been likened to the sun²³, in keeping with the astronomy comparisons.
If you don't go for the sun, moon and stars thing, maybe an Olympic analogy would be better. Getting into the celestial kingdom is like getting a gold medal. Awesome!! Getting into the terrestrial kingdom is like getting a silver medal - still great, but not as good as the gold. And the telestial one is like getting a bronze medal. Not as good as the gold and silver, but hey! You're still on the stand. The ones who don't get to be on the stand at all are the ones who deny the Holy Ghost.
I hope this clarified some things for you! Thank you for reading!!! I leave all these things in the name of Jesus Christ, amen.