Unlike hybrid seeds, heirloom seeds have a rich pedigree that enables them to produce true to type. If you save seeds from one plant and then plant those seeds, they will produce a true replica of the parent. If you save and plant the child's seed, you will again get a true replica of the parent and plant. While there may be slight variations, heirloom seeds will continue to produce true to type plants generation after generation.
Seed saving makes the gardener part of the living legacy of traditional methods of farming and ensures a consistent crop, year after year.