A paramour is a lover, and often a secret one you're not married to. So it's best not to kiss and make eyes at your paramour in public, unless you want to be the center of a lot of gossip.
The noun paramour evolved from the French phrase par amour, meaning “passionately” or “with desire.” If you break it down, you get par, meaning "by," and amour, the French word for love. Once upon a time, women used this word to describe Christ, and men would use it to refer to the Virgin Mary. But eventually, paramour shed its religious connotations and came to mean “darling” or “sweetheart,” and later “mistress” or “clandestine lover.”