The "shruggie" is an emoticon, depicting a person smirking and shrugging at the same time, that is becoming increasingly ubiquitous on the internet and especially on Twitter.
Its vertical orientation and its use of the Japanese katakana character ツ ("tsu") classifies this emoticon as a Japanese-style kaomoji.
However, in recent times the shruggie is far more common on the English-speaking internet than the Japanese speaking internet, which is surprising given how hard it is to type on phones and keyboards not configured for Japanese language input. It seems that most English speakers simply copy and paste it, although some dedicated exponents of the shruggie maintain a special input macro in order to have it ready to go at a moment's notice.
The exact meaning of the shruggie is somewhat opaque and hard to pin down. In general, it carries a meaning of throwing one's hands up, just as it depicts, but what exactly this means is always somewhat open to interpretation. It seems to convey a sense of ennui, weary bemusement, and grudging acceptance along the lines of the English phrase "it can't be helped," or in some cases, "guilty as charged." The idea is that you understand that there is something wrong on the internet, but you accept/admit that either can't or won't do anything about it.
In practice the shruggie often becomes a conversation ender. When somebody accuses you of something, or asks why you don't care more about some grave problem in the online world, sending them a shruggie instantly communicates that you simply don't want to talk about it anymore. In this sense, the shruggie is a deeply nihilist form of expression.
The shruggie is also deployed like a badge of honor. Its vague meaning, general obscurity to the general public, and the near impossibility of typing it using normal means in the English speaking world make it a kind of marker or sign delineating one's social status as an internet deep insider.
In sum, the shruggie is difficult to understand, annoying to receive, impossible to type, and deeply cynical and even nihilistic. In other words, it may well be the perfect emoticon for the present age.