Open pollinated simply means that the plant has been stabilized through many generations as opposed to a an F1 hybrid which is a first generation cross. Hybrids tend to revert to the parent plants and are therefore said to not come true from seed. Open pollinated plants if not cross pollinated will produced seeds that replicate the mother plant.
"Heirloom" has become a catchy word that has multiple definitions. They are open pollinated but that is about the only consistant component of the definitions.
Saving seeds takes some precautions as cross polination takes place more in some species than others.