If you have competency in something, you're well-qualified to do it, whether that's baseball, business management, or underwater basket weaving.
Competency means "capability." Although we use it to mean someone has a sufficient qualification, it comes from the word compete, meaning that someone with competency is good enough to compete with other candidates. If you pass the medical board exams, then you have medical competency. Most jobs require that you show competency, either through certification, or on-the-job performance. If you keep faking injuries to get out of saving people, someone will eventually question your competency as a lifeguard.