The Romance languages are the family that derive from Classical Latin. It's important to note that they are not called the Romance languages because they are romantic, though certainly some of them (Italian in particular) do lend themselves especially well to the arts of romance. They actually get their names from being derived from languages spoken by Romans. The word "romance" with a small "r" has the same origin, as it meant a verse written in the vernacular - that is, the Romance languages - as opposed to in Latin. The meaning only morphed later on to refer specifically to a certain sort of love or love story. So Romance came first, and romance later!
The Romance languages are found all over Europe, and due to later empires, now all over the world. The fullest extent of the Western Roman Empire left a legacy behind it that was carried by these civilizations to the corners of the globe. This means that the Romance languages are among the most-spoken on the planet. There are also Eastern Romance languages, though none of them originally extended outside Europe. The happy result of this is that if you learn a single one of them, picking up a second or third will get a lot easier - and if you know Latin, then arguably you already know a little piece of each! How well do you remember them?