What happen if a flower was picked off a plant?

Well it depends on the plant. Generally you want to deadhead a old flower to force other flowers to bloom. But this means that there will not be seeds. Sometimes this is a good thing and sometimes this is not. For example, I generally deadhead my daylilies. But if I was hybridizing, I would not do this because I would want the seeds to start a new kind of daylily.