Hijo de papi means "daddy's boy." It is used in reference to a dude whose professional, social, economic, or political position is not the result of his effort or talent but a consequence of his daddy's intervention. An equivalent term is junior.
In the clip below from a cheesy soap opera, Roberta tells Diego he's still un hijo de papi. Pay attention to the rancor she coveys when she uses the expression, accompanied of juniorsazo--a more emphatic version of junior.