The word erotic derives from the name of the Greek god Eros (Latin: Cupid). He was the son of the goddess Aphrodite (Latin: Venus) who was the goddess of love. The Greek language distinguishes among several different types of love, agape (spiritual love), philia (friendship, companionate love), and eros (sexual love or attraction).
The English term "erotic" is an adjective meaning "sexual". If you describe two people as having an erotic relationship, that means a sexual one. Erotically is the adverbial form of "erotic". Adverbs are used to modify verbs and describe the manner in which the action of the verb is completed. Thus when two people are in an erotic relationship they are likely to think of each other erotically.