This is part of the reason that the term "climate change" is preferred, instead of "global warming." People see it getting unseasonably warm and say "global warming!" But then if it gets really cold in summer, they say, "Where's global warming if it's freezing out?"
The 1-2 degree increase in global temperatures is for the global average temperature. Why is this important? You've got a planet with oceans covering about 139 million square miles. Increase the temperature over this large area by a small amount, and you're going to get a lot more water evaporating into the atmosphere, which can further skew the way sunlight is absorbed by the various layers of the atmosphere, and by the ground.
The net result of this is unpredictable and unusual weather patterns.
Now, is this climate change a result of human actions, or part of a natural process? Carbon dioxide is a greenhouse gas, which helps prevent infrared radiation from escaping back into space. Nature locked up huge quantities of CO2 millions of years ago, which are now coal and oil. We are releasing this carbon dioxide back into the atmosphere. Is it enough to really be a problem? Maybe, maybe not. I feel though that if there is a natural climate change in progress, which could have considerable consequences on the way we like to go about our lives, it might be best that we not help it along.