Romantic orientation (also called affectional orientation) refers to an individual's pattern of romantic attraction based on a person's gender. For many sexuals, their romantic orientation and their sexual orientation are in alignment, so the gender(s) of the people they fall in love with are also the gender(s) they are sexually attracted to. For an asexual, who does not experience sexual attraction, it is their romantic orientation that determines which gender(s), if any, they are inclined to form romantic relationships with. A person may be aromantic or romantic, or somewhere in between.
Romantic attraction is separate from sexual attraction. Both orientations can be mix-matched.