A demisexual is neither primarily attracted to either sex, nor do they primarily desire to have sex. This means that a romantic demisexual is someone who, in layman's terms, looks for personality over sex by nature.
Primarily, the human will not be attracted to another human, but after being with another human romantically, feelings may begin to develop. This is further elaborated upon by Rabger's Model, which suggest human sexuality is created by four factors: Primary/Secondary Sexual attraction and Primary/Secondary Sexual desire.
Demisexuality is (apparently) a form of asexuality, related to gray-a.