That's the single definition of Thane. Thane is an Anglo-Saxon title, I believe. Why have the speific title of Thane in Skyrim when you're going to only utilize 50% of what the title comes with? (I have a feeling you'll get a nice little estate, with some bodyguards maybe, from a Jarl).
Of course, we don't know about all the Holds yet... We just know about Whiterun.
Spoiler
It's confirmed that you becomes Witherun's Thane after defeating a Dragon. And you earn a Housecarl, the possibility to purchase a house at Whiterun (for 5.000) and a Enchanted Axe (Axe of Whiterun). It's a Low-Level (Start of the MQ) Quest.