It's like that famous epigram, or if you prefer, philosophical reflection:
If a tree falls in the forest and no one is there to hear it, does it make a sound?
Likewise a question on a Stack Exchange website, if it has been asked but never answered, and never commented, was it ever seen? The badge offers a small consolation as it tells the OP that at least his or her question has been noted by the overlords in SE.
Like a tumbleweed that rolls aimlessly in the desert, an answered question on SE “tumbles” in the no answers column, abandoned and long-forgotten.

Etymonline says that tumbleweed, once spelled tumble-weed, is a compound noun derived from tumble + weed, and it gives 1881 as its first written instance. @Hugo's answer suggests that the term is older than that, possibly as long ago as 1858
But what was this skeletal plant called before the 1860s? @Sven Yargs's answer mentions ‘Russian Thistle’, which was also known as ‘leap-the-field’, ‘Tartar thistle’, and which German immigrants fondly called wind witch.

An Illustrated Description of the Russian Empire By Robert Sears, 1856. (published, New York)
An article from the Daily Mail (Nov 2013) contains this snippet of information
Some stories claim that it was brought to America by Ukrainian farmers, but it's exactly origins are tricky to pinpoint.
In the 1890s a legislator proposed that a fence be built around the state to stem the incursion, but a decade after it had first been noticed, it was too late and the weed had already found its way to Canada.
It quickly spread across the West and by 1885 it had reached California and in 1959 it was collected for the first time in Hawaii.
For an example of a tumbleweed question that later grew roots and set up home: see Helmar's question which earned four upvotes, attracted several users' comments, and an answer, but only after the tumbleweed owner edited his post. There is hope for everyone, after all ☺
19th December 2016
There is a WINTER BASH hat for anyone who answers a tumbleweed question. Only 158 badges have been awarded since 2013, so hurry and grab your chance to earn a pretty rare hat.
P.S I earned my lifesaver hat on English Language Learners.
P.P.S The OP must accept the answer.