Open pollinated means that the seed is produced by parents of the same type. Thus they breed true to their type. Such as one parent is Black Valentine bean and the other parent is too. Thus all the resulting seeds will grow out as Black Valentine beans. This breeding is by natural means, such as via wind, insects, birds, or by humans. Thus a gardener can create and save their own open pollinated seeds.
All heirlooms are open pollinated. But they have the added merit of being older varieties often maintained by families or small seed preservation companies. There are plenty of more modern varieties that are also open pollinatated, but they don't have the long history of an heirloom. These more modern varieties came about by either careful selection (choosing for a certain set of traits, or by taking a sport and breeding it), or by crossing two varieties and standardizing the new cross over several generations, thus stabilizing it into a new independent variety.
I grow lots of open pollinated veggies, simply because I like to save my own seeds. I especially focus on the ones with expensive seeds, like beans, peas, and corn. Their seeds are large and heavy, adding to the expense of shipping them here to Hawaii. I produce almost all my own bean, pea, and cowpea seed. The only time I buy more is if I'm trying out a new variety. I don't grow all that much corn at the moment, but I do save my Golden Bantam corn seed. This year I plan to also save a few other varieties, but corn is tricky. It's wind pollinated, thus will readily crossbreed. Special care must be take to produce open pollinated non-crossed seed for the next year.
Other open pollinated veggies I save seeds from include cilantro, dill, basil, broccoli, bok choy and other Asian greens, daikon, onions, eggplant, tomatoes, and peppers. I find that saving seeds from these veggies is easy.
What are some of my favorite OP (open pollinated) varieties? Off the top of my head, I come up with.....
... Bean -- Maxibel, Purple Teepee, Red Swan, Rocdor, and others
... Corn -- Golden Bantam
... Peas -- Sugar Sprint, Oregon Giant, Green Arrow, Sugar Daddy
... Asian Greens -- Tatsoi, Blues, Dwarf Bok Choy
... Lettuce -- Green Ice, all the romaines
... Onion -- Texas Super Sweet
... Pepper -- California Wonder, Cubanelle, Banana
... Tomato -- Roma
... Daikon -- Minowase
... Basil -- Genovese
... Dill -- Bouquet, Fernleaf
... Cilantro -- Slo-bolt, Santo
... Cabbage -- Caraflex