"HPLC" stands for "High Performance Liquid Chromatography" a technique in analytical chemistry that is widely used to separate components of a complex mixture in order to determine what components are present and how much of each component detected is there.
In our case, we are using this technique to understand the presence and metabolites of a cancer treatment drug. The detection limits are on the order of billionths of a gram in a milliliter of blood.
This technology is very important in pharmaceuticals, manufacturing, environmental monitoring, agriculture, forensics and many other fields.
A column is a small tube, usually metal, filled with materials that are designed to interact with materials through adsorption of the analyzes of interest in such a way as to slow their flow through the tube based on their structures and other properties. They range in size from a tiny "nanoflow" column that fits in the palm of a hand, to columns a few hundred cm in analytical labs. I have seen columns several stories high in industrial plants designed for the purification of industrial products like certain classes of drugs. (This is generally an expensive proposition, best avoided but sometimes necessary.)
There are literally tens of thousands, perhaps more, of such materials called "stationary phases" placed in columns to do these separations, designed for different classes of materials. It is a huge area of science on which whole careers are spent, designing stationary phases and commercializing them so as to make them available to analytical scientists.
The HPLC industry is on a scale of billions of dollars per year.
The class of compounds on which we are working is very unusual, and identifying a column to achieve the required separations in this matrix, blood plasma, was a huge challenge.
Wikipedia's page on HPLC is very good if you are interested in more information.