There are two categories of housecarl in The Elder Scrolls V: Skyrim: those who serve the Dragonborn at one of his/her homes, and those who serve the Jarls of the holds.
Dragonborn's housecarls[]
All the Dragonborn's housecarls are potential marriage candidates as well as followers.
Jarls' housecarls[]
A Jarl's housecarl acts as their personal bodyguard and rarely leaves their side.