Over the past week or so, I've noticed a number of articles and posts about the Arctic. There seems to be some kind of ongoing flap about some climate change deniers denying that the extreme north is warming. I have (mostly) avoided reading those original posts because they can't be a good use of time (one example will essentially prove my point). Following each denier rant seems to be a barrage of posts refuting their claims. The good things about these posts are that they more carefully present evidence to support themselves and the reader can actually learn something from them (here's a good example from Tamino). Unfortunately, I don't think these posts help to convince the public of the state of the science, since the public doesn't read them (sorry, but they don't). If a person is willing to dig into the climate change issues enough to read these posts, I think they have already decided what they believe before they get involved (even passively) in these "debates." (They are, of course, not debates at all.)
Another article from the NYTimes.com helps explain why the warming Arctic is an important issue, not just for climate research, but for geopolitical and economic reasons. A commercial ship is about to finish traversing the Northeast Passage from South Korea to the Netherlands. This cuts thousands of miles off the usual trip. If more ships start going this way during the summer, Russia stands to profit because the ships will sail through Russian waters. The path has historically been blocked by ice even in the summer, but as the Arctic has warmed, summer ice has become reduced in area and thickness, and over the past few years the Northeast Passage has been open for a few weeks each year. Similarly the Northwest Passage through Canada's many islands has been open, but so far commercial ships haven't used it yet (they will soon, I would wager). These are impacts of climate change, and unlike most other impacts, these ones could be interpreted as positive for some of the involved parties. Of course, along with these routes opening, the open waters spell doom for the polar bears who have become unwitting symbols of the ecological impacts of a warming world.
On the research side of things, the warming Arctic has long been considered the proverbial canary in the coal mine. Because of strong positive feedbacks associated with snow and ice retreat and atmospheric water vapor, there has emerged a general understanding of the polar regions (especially in the north) as being particularly sensitive. The poles are expected to warm most rapidly, an effect usually called "polar amplification." There is some scientific uncertainty about whether the amplification is observed yet (e.g., this RealClimate post from C. Bitz), but there is strong consensus among researchers that it will emerge from the noise. This view is supported by climate modeling experiments, in which all the reliable models predict an amplified response in the Arctic. From my reading, which is incomplete, this extends to the Antarctic, but only on slightly longer timescales because of the heat transfer into the Souther Ocean.