Proteins are made in nature out of just 20 amino acids. Those 20, strung together like beads on an unusually sticky necklace, do essentially all the work that keeps us (and everything else on the planet) alive. It’s easy enough to hijack the machinery that makes these proteins to make any artificial protein we might dream up. But sometimes, 20 isn’t enough, and we humans decide that we’d like to make a protein that’s got something else in it, something that nature didn’t think of.
The most common application of this is probably drug development, where you want small molecules that do something extremely specific. Usually, you want a protein that’s at most 15 amino acids long. Once upon a time, the way to do this was old-fashioned chemistry. You start with a bunch of chemicals in solution. You mix them together and they react, and then you filter out the product you wanted from the soup of useless junk, and repeat. This sort of reaction and separation has to be done once for every stage of the protein synthesis, or 15 times, in this case. In the 1950s, that meant about 5 years to complete the reaction.
In 1959, a chemist at Rockefeller University in New York solved the problem. Instead of using free-floating mixtures, the first amino acid in the sequence was attached to styrofoam beads. Subsequent stages added more amino acids to the chain, but the product did not have to be filtered out after each step; it was stuck to the bead. All the junk was still in solution, and could simply be drained away. Synthesis went from PhD theses to routine lab work.