Heirloom seeds refers to seeds that are worth saving, to be passed on to the next generation, in just the same way that heirlooms of any type are passed on. Heirloom seeds are the originals, they grow true to form and have not been selected for specific qualities or hand-pollinated, as hybrid seeds are. Heirloom seeds are fertile when harvested from the plant (unlike many hybrid seeds).
Heirloom seeds may also have a better flavour, texture, colour, etc., than hybrid varieties. This depends on the plant type and, on occasion, subjective interpretations. However, many people do find that some crops, such as tomatoes, taste far better when grown from heirloom seeds in gardens or small farming operations than from the supermarket varieties grown on a large scale.
Many older varieties of plants are threatened with extinction, which may be as good a reason as any to term them heirlooms, in need of restoration and growing again.
While heirloom seeds are fun and useful to grow, they can meet problems that require experienced gardening know-how. For example, changes in the environment, soils, atmosphere, etc., may make it harder for some heirloom varieties to grow, while pest problems may have increased since the variety was once grown. In this case, trial and error may be required to learn the optimal growing conditions for your particular garden.