The botanical definition of an heirloom tomato is simply any open-pollinated variety, as opposed to a hybrid variety of tomato. That is, pollinating the flower with pollen from a plant of the same variety makes fruit containing seeds that will reproduce the tomato, true to type. Growers can save seed from their crop and sow again in following years. The seeds can be passed down so they become ‘heirlooms’, a prized variety from the past still popular today.
And perhaps this is the "social" definition of an heirloom tomato: an open-pollinated variety that has been kept in a family or achieved a measure of local or regional fame. Many heirloom types are immigrants--cherished varieties that can be specifically tied to a group of people and were brought to America by early settlers. The preservation of these seeds was not due to sentimentality, but because these were time-tested varieties bearing an implicit seal of approval. Heirlooms represent, quite literally, the interwoven fabric of both natural and human history. It's pretty fascinating
And the economic definition of an heirloom is simply any open-pollinated tomato that has the characteristic exciting stripes, colors, irregular shapes and strong flavors we associate with "heirloom tomatoes" -- regardless of historical lineage. Many people today still breed new open-pollinated varieties. Some the ones I grow were created recently (check out Wild Boar Farms), while others are perhaps 100 years old.
I buy grafted tomato transplants, and when the grafter ordered seeds for what she thought was a strain of the classic "brandywine" she unknowingly bought seeds for an unrelated plain red tomato--we were both surprised. This red tomato is in fact an heirloom by the cultural definition, but has little value because it is red like a regular tomato. I suppose it doesn't meet the "aesthetic" definition either. And while we're at it, yes, there are hybrid varieties that have the heirloom tomato "look" but are actually botanical hybrids.
So in the end, the idea of an "Heirloom Tomato" might seem perfectly clear only until we actually know something about it -- kind of like a lot of things in the world, perhaps!