There are many themes and conflicts in Lois Lowry's The Giver, but the most predominant one would be the conflict between individualism and social conformity--in other words, man versus society.
In the community in which Jonas dwells, nothing is left up to chance. All elements of human life are strictly controlled and ritualized, creating a highly insular environment in which men and women are assigned spouses, jobs, rest days, and even non-biological children. Residents are not allowed to experience "stirrings" (or sexual feelings), do not marry for love, do not produce their own offspring, and are "released" (euthanized) when they reach old age. They also are incapable of feeling emotions and are unable to see color. In other words, their lives are highly compressed, regulated versions of a normal human life. They have forfeited individualism for "sameness."
After Jonas is named as the next Receiver, he is given the banished memories of the community--their joy, sadness, pain, love, etc. Realizing the truly dimensional human experience that his fellow residents are missing, Jonas decides that he must escape the community in order to release these memories back to their rightful owners. So, while the focus here is on man versus society, there is also an element of man for society; Jonas must defeat these rules by abandoning the community that has restricted people for so long, therein saving that community.