So the long term prediction for the climate is that it'll become 2°C hotter worldwide - on average. "Big deal", I hear the sceptics say, "between January and Juli, we get 30°C difference. How much is 2°C is going to add to that? A mere 6%!"
If the climate was a linear system, the 6% would be correct. But the climate is not a car which accelerates smoothly. It's a complex system. Let's look at a really simple complex system, called the Lorentz attractor:
This is a file from the Wikimedia Commons which I got from the Wikipedia article mentioned above.
The Lorentz attractor is not a perfect example because it's not actually a system that flips rarely (if you follow the curves, you'll see that they go back and forth between the two points all the time instead of staying with one side for some time as our climate does).
Still, it's a good way to visualize what is going on. Imagine that the lower disc with the fat red circle in the middle is the current weather. Temperature is pretty stable around one spot. Now the system gets jolt and starts to move out of the current equilibrum.
Instead of just dropping into the next equilibrum 2°C away, it starts to move in strange patterns. Instead of the temperature simply raising until it's 2°C hotter, it's sometimes much colder, sometimes much hotter. And the change is also not a smooth one. The farther the curve is from the two stable points, the faster it travels. Which means that within a few days, the temperature can drop and raise sharply.
Last week, we had temperatures at 900 in the morning between -1°C and 7°C, a delta of 8°C withing a week. And that's not the lowest and highest overall temperature, it's the temperature measured at the same time in the morning.
You should start to worry about the 2°C because they mean we'll see natural disasters like man has never known before while the climate adjusts to the new average.
Or to put it another way: 2°C means that the earth becomes more hot. It means, if the earth was on a stove, someone is adding more heat or energy to the stovetop. If the earth was a pot with water, that energy would amount to 10.471 zettajoules (one zettajoule is 1 times 10 to the power of 21J) which is roughly the same as the energy the whole earth receives from the sun every day. As a number:
The energy released by an average hurricane in one second is a meager 6 terajoule which is a billion times less. Imagine what power a hurricane could get from an athmosphere which has so much more energy to lay waste to our civilization?