To suppurate is to get infected and form pus. If that scrape on your knee starts to suppurate, you might want to go to the doctor.
In medicine, suppurate is the official term for what you might think of as "become gross and full of pus." Pimples sometimes become swollen and painful before they suppurate, and cuts and scrapes that get infected can also suppurate, oozing a thick, white substance. We can trace this word back to a root that means both "matter from a sore" and "bitterness or malice."