In 1928, British bacteriologist, Alexander Fleming accidentally discovered the first true antibiotic, Penicillin. He noticed that the fungi he had isolated, Penicillium Notatum, was stopping the growth of bacteria on a petri dish. He was later awarded a Nobel prize in medicine for his work.
Prior to the discovery of antibiotics in early 19th century, treatable infections by today's standard, killed millions of people across the world. Basically, anything which could lead to an infection could kill. Scientists relentlessly tried to discover new ways to make things better and began the "hunt" for finding powerful remedies. The work on antibiotics was built on the belief that "there had to be a better way".
At the beginning of the 19th century, scientists started working on moulds because their anti-bacterial properties were intriguing. A little bread mould was capable of "tackling down" aggressive bacterial cultures. They realised when moulds were put next to bacteria cultures, not only did they kill the bacteria present, but they also prohibited any further growth. The bacteria activity was simply "halted".
In 1928, Alexander Fleming, who is popularly known as the father of modern day antibiotics, was observing an experiment on Influenza virus. He noticed that there was a halo around the bacterial culture, which inhibited the growth of bacteria, while the surrounding area on the dish was normal. This led him to infer that something must be stopping the bacteria from growing in the area of the halo.
Upon further investigation, he discovered that the halo contained a common fungus called Penicillium notatum and it could suppress bacterial growth by "breaking down" the bacteria.
The first sample of penicillium mould isolated by Fleming is still intact and stored in "Alexander Fleming Laboratory Museum" in London. By the late 40's, mass production of Penicillin for medical use began. This was a huge milestone for modern medicine.
Ever since the discovery by Fleming, much work has been done on antibiotics, and it was then formally defined as "substances that inhibit and stop the growth of bacteria". In 1943, Selman Waksman, the microbiologist who discovered Streptomycin, first used the word "antibiotic" in the medical context.
Many powerful antibiotics have since then been developed on the basis of penicillin, and the "accident" itself remains a beautiful and memorable one.