Because they are a cross between varieties, the seed produced by hybrids will not grow true to seed. Seedlings grown from a hybrid could exhibit traits of one or both parent plants or be something totally surprising.
There's nothing unusual about creating hybrid plants. It happens in nature all the time, when two different species cross pollinate. Commercial hybrids come about after a great deal of work.
For the initial crossing, pollen from one plant has to be transferred to the flower of another variety. Before doing so, the breeder has to decide which plant he wants to use as the female (the pistil) and which he wants to take pollen from (the stamen, male parts). Then all the stamens have to be removed from the female plants, so they don't self-pollinate. The fruits that form as a result of this cross pollination are harvested and the seeds are collected.
This process has to be repeated every year. First time crosses are grown out the following year and the fruit they produced is evaluated. If it meets expectations, the cross will be repeated and the seeds will be marketed the following year. But it can take many years before a hybrid with the desired traits is even created. If the resulting fruits are disappointing, the breeder is back to square one.
But even when the breeder has a winner, the process continues. Seeds for the popular commercial hybrids, like 'Sungold' and 'Early Girl' tomatoes, have to be crossed, harvested and saved every year. These are called F1 hybrids, for first generation, because they are the direct product of a cross. The breeder who first creates a hybrid owns the rights to it, which is why they can be more expensive than non-hybrids. They guard the parentage of their hybrids closely.
It is possible for hybrids to stabilize and become open pollinated plants. This generally takes many years and careful selection of plants with exactly the traits of the original hybrid.