From A Wiki of Ice and Fire
A paramour is the unmarried lover of a noble. Dorne gives a degree of social status to paramours, despite the "unchaste" nature of the relationship. Outside of Dorne, a paramour's status is less certain. They may be afforded the esteem granted in their homeland by the diplomatic minded, or they may receive a range of treatment from slight social disdain to moral condemnation.
The most notable paramour presented in the series to date was Ellaria Sand, to whom a degree of social deference was expected by virtue of her relationship with Prince Oberyn Martell. While esteemed as a high-ranking woman by the Dornish, in King's Landing her presence at the high table at the wedding of Joffrey Baratheon and Margaery Tyrell would have been taken as an insult by the noblewomen seated near her. Cersei Lannister and Olenna Tyrell referred to her as a "whore."
It was a closely held secret that Prince Lewyn Martell kept a paramour despite the Kingsguard oaths of chastity. Ser Barristan Selmy and his other sworn brothers were aware of this but kept their sworn brother's secret. Daario Naharis is considered to be Daenerys's paramour.