The same reasons why any FE characters is liked. No particular reasons, but I fell for (during my most hardcore 2d>3d days in high school) Lucina because main character status, good character, attractive design, the game had insert character available and said insert character can marry her. This is the perfect reason at least to me why she is so popular, adding to the facts that her game was the most popular.
She single handedly converted me from the old FE to the new. I loved Lyn, Hector and Eliwood as much as any veteran. Mark x Lyn was my old OTP until Robin x Lucina came to light.