First of all, its heritage is very strong, and goes back a long way. Infinity Ward, the developers for the original Call of Duty games and the Modern Warfare games, was founded by part of the development team for the Medal of Honor games. This is a team that have been making popular first person shooters since 1999. The Call of Duty brand itself has been around since 2003, with Modern Warfare 3 being the 7th game by Infinity Ward in the series, and it has steadily been picking up recognition and fans. It didn’t see really mainstream success until around Modern Warfare, which was the fourth game in the series to bear the name. While more recently Treyarch have also developed some of the Call of Duty games, they haven’t shaken up or made the large steps forward that Infinity Ward have, and only became involved after the games were starting to see their mainstream success.
The second point is that this is a genre that appeals to a demographic that already buys a lot of video games, i.e. males 18-30. This is one of the largest demographics for video game sales, and the Call of Duty games do very well to appeal to it. Of course there are players outside of this demographic who also enjoy the game, but the fact that it has a strong core audience is definitely not going to have hurt sales or hurt its spread.