Romance is a word of many historical meanings. Starting with the Chivalric Romance, where it meant "work written in the vernacular."
From that, it derived the meaning of tales of drama, adventure, and larger than life characters and often magical elements and strange monsters. Hence, writers speak of Shakespeare's romances, and Planetary Romance, and Ruritanian Romance. It is the source of the name of Romanticism.
To this day, "romantic" is used as a contrast to "realistic" from the movement. This can reflect anything from pure magic to the use of atypical, exaggerated characters for heroes and villains, clear conflicts, and definite resolutions.
It is also used as a contrast to "classical"; in the tradition of the chivalric romance complicated plot threads and sometimes Random Events Plot, it, in this sense, denotes works with a wild miscellany of events, a luxuriant degree of detail and complexity (not necessarily organized), in contrast to an aesthetic of simplicity and purity.
But nowadays, the most common meaning is that the Romance genre is about people falling in love. See Romance Novel for more and Love Tropes for many tropes typical of this definition.