An IBM-compatible PC (often shortened to PC) is the term used for a personal computer which is compatible with the IBM PC line of personal computers (in the sense of 'it will run all the software for the IBM Personal Computer'). IBM no longer makes PCs, but the terminology persists.
Compaq was the first company to make a machine which could run any and all software for the actual IBM PC. Once these machines appeared, they rapidly drove out the other PC's which were not IBM-compatible, as the latter often required custom (and low-volume) versions of software.
Nowadays, other than personal computers from Apple, essentially all personal computers follow the IBM PC standard.