There are four major different eternal destinations after this life according to Mormon doctrine:
The celestial (heavenly) kingdom or glory. Those who have faith in Jesus Christ and obey his gospel (see Doctrine and Covenants 76:50-70).
The terrestrial (earthly) kingdom or glory. Those who are honorable people but have not proven faithful enough. For more details see Doctrine and Covenants 76:71-80.
The telestial (distant) kingdom or glory. Very roughly, those are the bad people. Yet the glory of the telestial kingdom "surpasses all understanding" (see Doctrine and Covenants 76:81-90,98-106).
Outer darkness. Those who commit the unpardonable sin of denying the Holy Ghost after having received a full knowledge and a perfect witness of the truthfulness of the gospel including Satan and his fallen angels (see Doctrine and Covenants 76:25-39). Only very few people living on the earth will end up there.
I only wrote roughly who goes where, but in the given references it explains more detailed the requirements and the state of these glories. The most interesting place is the celestial kingdom. Accoding to LDS doctrine the gospel of Jesus Christ requires one to
- have faith in Jesus Christ and His atonement,
- repent of their sins,
- be baptized by immersion,
- receive the gift of the Holy Ghost by the laying on of hands and
- keeping the covenants they have entered into until the end
in order to enter the celestial kingdom. There are many who did not have the chance to do these things. Here the following scripture applies (see Doctrine and Covenants 137:7-10):
7 [...] All who have died without a knowledge of this gospel, who would have received it [...], shall be heirs of the celestial kingdom of God;
[...]
10 [...] all children who die before they arrive at the years of accountability are saved in the celestial kingdom of heaven.
Therefore, we do not baptize little children until they can make a conscious decision.
Furthermore the celestial glory itself has three degrees (see Doctrine and Covenants 131:1-2):
1 In the celestial glory there are three heavens or degrees;
2 And in order to obtain the highest, a man must enter into this order of the priesthood [meaning the new and everlasting covenant of marriage];
In practice this means that the highest degree in the celestial kingdom can only be received, if a man and a women are sealed (married) in an LDS temple. The same principle as in Doctrine and Covenants 137:7-10 applies here.