All gardens start with seeds, and flipping through seed catalogs you'll see listings for seeds that are "hybrid", "open pollinated" or "heirloom." Both hybrid and non-hybrid seeds have their advantages and disadvantages, and knowing the difference between the two will help you choose the seeds that are best for your garden.
To produce hybrid seeds, two distinct varieties of a plant are bred together to produce a new variety that incorporates some of the desirable characteristics of the two parent varieties. The fruits and vegetables that come from hybrid seeds may ripen earlier or produce more uniform fruit, or they may be more resistant to diseases or pests. But the seeds from hybrid fruit won't produce the same variety of fruit as the parent plant, or the seeds may even be sterile. Many hybrid seeds are created in the field by planting two varieties close together and intermixing the pollen. Many states in the US require that hybrid seeds are labeled as "hybrid" or as "FI", which denotes that the seed is the first filial generation.
Another way to create hybrid seeds is through genetic modification. Genetically modified (GM) seeds are created in the laboratory by introducing DNA from one organism (a fish, for example) into another organism (a tomato). GM seeds may also have pesticides inserted into their DNA so that the resulting plant is pest resistant. As of this writing, GM seeds are available only to large commercial growers, not to home gardeners. The resulting fruits and vegetables from genetically modified seeds are not required to be labeled in the United States.
Open pollinated (OP) plants are varieties that have often been passed down from gardener to gardener for years. Open pollinated seeds are cross bred plants that have stabilized and will produce seeds that grow true to the parent plant. Open pollinated seeds will adapt to their growing environment over generations, so if you decide to save your own seeds you choose the seeds that grow best in your location.
Heirloom or Heritage Plants
The terms heirloom or heritage do not have a legal definition, but they are generally used to denote seed varieties that that been grown since before 1950, although some people may use an earlier cut off date. Heirloom varieties of fruit and vegetables are often tastier and more nutritious than modern hybrids, but they may not be as pretty or won't travel well.
The gardener interested in saving her own seeds to use next year should always choose open pollinated seeds and plants, and there are many seed catalogs that specialize in open pollinated varieties. If you're growing two varieties of the same kind of plant, grow them far apart from each other so that they won't cross pollinate each other and the seed will stay true.