I'll break it down because this is one of the first questions I had about tomatoes. The following is what I have learned through a lot of reading and posting to message boards where noted experts mingle.
Below is a simplified
version because more than 2 plants can be used to create a hybrid.
Variety A shares pollen with Variety B.
The seed is saved from the proper fruits and this seed is (F1).
The F1 seed is grown and Variety C is created. This plant is the one you buy or this seed is the seed you buy.
The plant grows and if you save the seed it is F2.
If you grow this (F2) seed you get genetic unpredictability, and even though you can stabalize it over many years, you will likely never get more than 80% of the genes from the original (according to a well-known PhD tomato breeder who created several widely known hybrids).
Therefore, you can only get the same results by crossing the original two varieties and growing from that F1 seed.
Hybrid F2 seed will grow and is viable, it's just that it is not predictable.
Many people do try to save seeds from hybrids in order to attempt to stabalize them (you can stabalize through growing a bunch of plants and only keeping those that are similar to the original and then doing this over and over again for years -- this is a simplified version of it). Once these plants become predictable, (or stable) you may have something like the original variety but probably will never ascertain more than 80% of the original genes, as I mentioned above. This is one reason why some hybrids are never stabalized since one may not be able to acheive the result of the original cross. As a result, the retailers just sell plants or seed that were the result of a direct cross (F1). Many hybrids are a trade secret and the companies that create them often keep the identities of the parent plants under wraps. The genetic lineage of many well-known hybrids is known today since some companies have went out of business, breeders have retired etc. If the identity of a hybrid's parent plants is not released and the breeder stops producing them, then they are mostly lost forever unless you stabalize the F2 seed, which, again, will not give identical results.
Remember that almost all modern tomatoes were once hybrids. Again, over time a hybrid can become stable either through natural segregation or through human control. Once a plant becomes stable, it is considered "OP," and this is what you get with heirlooms. Heirloom seed gives the same results over and over (no matter the generation of the seed) assuming the plant was not accidentally crossed in your garden. Most heirlooms were the result of natural or accidental crosses that occured many plant generations ago. That's the difference -- heirlooms have been stable for generations and hybrids are the result of recent crosses.
Some people debate what is an heirloom and what isn't. There are some tomatoes that were developed 75 years ago or more and have been stable for decades that still are not considered heirlooms, while other plants are much more recent stable crosses and are considered heirlooms.
I am no expert on this, but I feel the above explanation is a fair one and is at least good enough for us laymen.