Perhaps the most famous outcome of biotechnology is penicillin. It was discovered or invented, depending on the point of view, by Alexander Flemming in 1928. However, the story of the discovery actually goes back many previous decades before this. The French doctor Ernest Duchesne found that glaucum, from which penicillin is derived possessed healing properties, though he did not make the connection, which would be done by Flemming, 30 years later.
Flemming discovered that if penicillin was grown under the correct conditions it would secrete a substance that had healing properties. The discovery was said to be an accident and that Flemming was growing another substance which he left by an open window and it was affected by some blue and green mold. He found where the mold had grown on the petri dish, it stopped the growth of the harmful substance.
Once he observed this happening, he decided to grow a pure version of the mold. This is where biotechnology comes into play. He knew that the mold possessed healing properties but clearly you cannot administer mold to somebody who requires the antibiotic. Therefore, the substance had to be artificially generated in a form that was useful to humans and could be used as the highly successful antibiotic that we have come to use so prolifically in modern medicine.
It is said that Flemming was a poor communicator and thus he had issues at first convincing people that the substance would be useful in treating infections. It was not until several years later when the discovery was picked up by Cecil George Paine and used to treat infections that the discovery was hailed as a resounding success and it started to become one of the most commonly used medicines in the world. It also paved the way for more antibiotics to be discovered.