A key technology in modern biology.
A monoclonal antibody is a preparation of antibody that all have the same exact specificity, and in fact, is all the identical protein.
When vertebrates are vaccinated with an antigen, one of the responses that the immune system comes up with is to make antibodies to the vaccine. Because many B-cells are responding at the same time, the blood of the vaccinated animal contains many different antibodies. Even the antibodies that actually bind the antigen are all different, and potentially bind different parts of the antigen.
For an immune response to a pathogen, or for having a good response to a vaccine, this is not important. But researchers have known the potential use of antibodies as a tool in research. Since vertebrates can make antibodies that bind to pretty much anything, making a specific probe to bind a molecule of interest is potentially as simple as shooting whatever you want the antibody to bind into a rat.
Monoclonal antibodies are made in such a way as to obtain antibodies that are all the same and see the same antigen in the same way. Basically, one immunizes an animal, removes their spleen and purifies the B-cells that make antibodies. These cells are then separated from one another, and each are fused to another cell that confers the ability to replicate and survive outside of the animal. The culture supernatants of these hybrid cells are tested for the antibody that you want. Once you find a hybrid cell making the antibody you want, you can grow as much of the now monoclonal antibody as you need.
Niels K. Jerne, Georges J.F. Köhler, and Cesar Milstein all won the 1984 Nobel Prize in Medicine for coming up with this technology.
The writeup below talks about the biomedical uses of monoclonal antibodies, many of which didn't pan out. Monoclonal antibodies have proven fantastically useful, however, in the pursuit of molecular biology. As the method let's one make monoclonal antibodies to any particular molecule, the monoclonal antibody itself is used to determine if the antigen exists, whether in a particular sample (Western blot) or on the surface of a cell (FACS). The antibody can even be used to purify the antigen it was raised against (via immunoprecipitation, or chromatography techniques).
Monoclonal antibody production not only gave us great insights into the biology of B-cells and antibodies, but provided one of the key techniques that have helped the progress in biological sciences for the past 20 years.