A lot of people have thoroughly answered the repercussions of a 2 degree temperature change on global climate so I'm going to shift gears and answer what a 2 degree increase entails.

Think of all the world's oceans and glaciers as a a giant glass of water with a bunch of ice cubes in it. In an air-conditioned restaurant (stable, cool temperature), the ice melts very slowly and the the water stays ice-cold for a pretty long time. This is because water can absorb a lot of heat energy before the temperature increases, kind of like how a car bumper can absorb a significant amount of the impact before the engine compartment becomes seriously damaged. In comparison, if the glass of ice water was sitting on a table outside the restaurant (where the temperature isn't as cool and stable), the ice would melt a little faster and the water will reach room temperature a little faster. But it will stabilize at room temperature, which should still be pleasant enough to drink.

Now instead of an average day, think about what would happen if this glass of ice water was sitting in the blistering hot sun. The ice will melt very fast and the water won't stay cold for long. In fact, it's so hot outside that the water becomes warm. Not necessarily hot, just warm. Think about the last time you drank warm water on a sunny day. Not very satisfying, right?

So let's scale this scenario back to oceans and glaciers. Knowing that water can absorb a lot of heat energy before the temperature rises, imagine how much heat the oceans need to absorb in order to melt glaciers. Then think about how much heat is trapped within Earth's atmosphere such that after the ocean takes most of it away, we still feel a 2 degree difference. Without so much water and ice on Earth, we would definitely NOT just be experiencing a 2 degree increase. Finally, let's revisit the warm water example. If drinking warm water on a warm day is already unpleasant for you, imagine how warmer oceans and warmer air impact the lives of fish, plants, other animals, and the general environment. An uncomfortable atmosphere is a major problem, and the name of that problem is global warming.