In The Giver, what does the community gain by not having memory?

Because the Receiver holds all of the collected memories for the community, the members of this society have no sense of history. This means that they have no memories of conflict that could drive further conflict. They are not burdened with the sadness or grief of past events. They also don't know the benefits of living any other way and can't recognize the benefits of living in a society which doesn't, for example, release the elderly or newchildren who aren't thriving. They peacefully exist in the society created for them because they have no memory of other societies.
In short, by not having access to memories, people peacefully accept their present society as the only way to live.
Of course, the point of Jonas's experience is that everyone needs the pain of the past in order to make the best possible decisions. Without knowing pain, they also can't really know other emotions, like happiness or love. The human experience is dependent on fully living through all past experiences, including the painful ones.