Heirloom vegetables are not a special species of plants. The term heirloom vegetable is used to describe any type of vegetable seed that has been saved and grown for a period of years and is passed down by the gardener that preserved it. It has a provenance, of sorts. To be capable of being saved, all heirloom seed must be open pollinated.
Open pollinated or OP plants are simply varieties that are capable of producing seeds that will produce seedlings just like the parent plant. Not all plants do this.
Plant breeders cross breed compatible types of plants in an effort to create a plant with the best features of both parents. These are called hybrids and many of our modern plants are the results of these crosses.
While plants can cross-pollinate in nature and hybrids repeatedly selected and grown may eventually stabilize, many hybrid seeds are relatively new crosses and seed from these hybrids will not produce plants with identical qualities.
For example, each year new hybrid tomato varieties are offered. You may see them labeled as hybrids or F1, first filial generation (first-generation hybrid), or F2. These may eventually stabilize, but for the moment a tomato like the popular 'Early Girl' does not produce seeds that reliably have the features you expect in an 'Early Girl' tomato. Seed from hybridized plants tends to revert to the qualities of the parents, so tomatoes grown from seeds saved from your 'Early Girl' tomatoes might still be tasty, but not so early.
Anyone can select and eventually stabilize their own seed or even hybridize new plants, but plant and seed companies have recently begun patenting their crosses so that only have the right to reproduce the hybrids they've developed.
Hybrids should not be confused with genetically modified organisms or (GMOs) which, according to About.com's Biotech Guide, can be any plant, animal or microorganism which have been genetically altered using molecular genetics techniques such as gene cloning and protein engineering. Plants like corn that has the pesticide Bt engineered into its genetic makeup to make it resistant to certain pests are GMO crops. Bt is a natural pesticide, but it would never naturally find its way into corn seed.