If you have competence, you're qualified or well prepared to do something. A driving test will show if you have competence behind the wheel.
If your dad discovers a new dent in his car each time you've borrowed it, don't be surprised if he questions your competence as a driver. The words competence and competency are sometimes used interchangeably, although competence is better when describing the quality of being well qualified. Competency is more appropriate in a legal sense, referring to the ability of a person to make decisions or stand trial.