In the biological/scientific world a hybrid is the offspring from two different species, but in the gardening/agricultural world a hybrid is any first generation offspring from two different varieties of the same species (our parents would be considered different varieties and we would be called hybrids), for instance crossing Brandywine with Cherokee Purple would give you hybrid seed and a hybrid plant, but if you took seed from that hybrid it would not be considered hybrid. This cross pollinating is usually done by hand, which is why hybrid seed costs more.
Seed from tomato plant parents of the same variety or from self pollinated plants are termed "open pollinated". All "heirloom" tomatoes are open pollinated varieties that have been selected over several generations to breed true, also termed "stabilized". If you take seeds from a hybrid the genetic combinations from the original two parent varities segregate and you will get different types of plants (not stable).
An example of this would be crossing a regular leaf (RL) red cherry (all 3 dominant traits) with a pink potatoleaf (PL) beefsteak (all 3 recessive traits). The hybrid offspring (f1 generation) would be a red regular leaf cherry. The seed from those self pollinated fruits (F2 generation) would be the following combinations in known proportions:
Red, RL cherry
Red RL large tomato
Pink RL cherry
Pink RL large tomato
Red Potato leaf cherry
Red PL large tomato
Pink PL cherry
pink PL large tomato
None of these would be stable (except maybe the pink pl large) because there might still be combinations of dominant gene alleles hiding recessive alleles...seed from the Pink PL cherry could yield both cherry and large fruits, but if you grew it out several times taking seed from the same type each time the chances of an alternate combination showing up is progressively reduced to almost nothing after a handfull of generations.
Even if you had a hybrid of two similarly looking varieties you have different "flavor", "health", and "disease resistance" gene alleles that will segregate out when you grow seeds from it.
Because not all traits are completely dominant/recessive, the mixed alleles in hybrids allow them to produce more consitently under a wide varity of conditions, and the fruits tend to be more uniform in shape. Heirlooms (OPs) may produce much more than a hybrid one year and less the next, and more fruits may not be nice looking enough to sell to someone expecting grocery store/Hollywood perfection (not good if you are a farmer stuck with the same costs year after year).