F1 seeds are produced by cross-pollinating two pure strain plants (types that have been self pollinated for many generations to emphasize beneficial characteristics, but are therefore usually fairly weak). The resulting seed will produce plants that have these good characteristics, but as they have come from cross (rather than self) pollination they also have something called 'hybrid vigour' which usually produces excellent plants.
Some people are reluctant to use F1 seed as the characteristics that have been bred in are often aimed at commercial growers, and therefore may be less suitable for amateur growers - e.g. sprouts all maturing at the same time. Also, the process is far from natural which puts people off. The use of these F1 seeds, reduces the use of traditional or heirloom varieties which are open pollinated (by insects). Seed collected from F1 plants will not produce the same crop as the origninal F1 crop, as these have been open pollinated, and so are unreliable for collecting your own seed - you have to go and buy more seed the next year.
While the process of producing F1 seed is essentially manipulating the genetics of the plant (in much the same way as pedigree dog breeds have been bred over generations) it is not Genetic Modification as is understood by most - i.e. biochemically inserting genes into the DNA of a plant like Monsanto do with wheat etc.
I use some F1's and some open pollinated seed. Horses for courses.
Finally, I have a feeling that Peer Gynt is no longer available.
Dave