Thane (Title)

"Then by my right as Jarl, I name you Thane of [Hold]. Congratulations. I grant you this weapon from the armory to serve as your Badge of Office. I'll also notify the Guards of your new title, wouldn't want them to think you're part of the common rabble now."

- Jarl [Name]

Thane is a rank given by a city's Jarl after the Dragonborn completes tasks, becomes accepted by the people of the city, and owns property in a city. The Thane is someone recognized by a Jarl as a person of great importance in a particular city, often a hero.

Benefits and requisites
The guards of the town excuse the Dragonborn from crimes if they mention they are the Thane in a dialogue option when confronted, but the amount of times this works is limited. After being proclaimed Thane in a city, the Dragonborn can purchase houses from the Jarls' stewards. In a few cases, purchasing a home within a Hold is a prerequisite for becoming a Thane of said Hold. Newly titled Thanes receive housecarls, who protect the Thane, their spouses, and their property.

Other Thanes

 * Erikur and Bryling serve as Thanes to Elisif, Jarl of Solitude. Melaran, an Altmer alterer, serves as their housecarl.
 * Dengeir of Stuhn, Former Jarl of Falkreath Hold now serves his nephew, Jarl Siddgeir, as Thane.

Real-world meaning
The Thanes (Thegns) were the minor and greater nobility of Anglo-Saxon England -- serving as leaders of the local militias, monitoring crime, and carrying out general work of their Ealdorman.

Thane