Merit is another way of saying "deserve." The National Merit Scholarship program is based on merit––students whose SAT scores are high enough deserve to be in the program. If kids seems to be getting in who hadn't even taken the SATs––that would merit an investigation.
You will often hear the phrases merit-based promotion and merit-based pay, which come up when employees are pushing against a system in which time on the job––and not job performance––determines when workers are promoted and how much they are paid. Using the word merit suggests impartiality and objectivity––such as when you swear off a prejudiced approach to something and vow to "judge it on its merits."