Scientists recently predicted that a change of 1.5 to 2 degree C can be a huge warning in the direction of climate change for this planet. Have you ever wondered why a change of ~2 degree C can be a big deal? Well the outside temperature changes by more than this difference almost every season? Where does the difference lie? Here are some points for people to clearly understand the nuances of climate change more clearly. All credit goes to the wealth of information provided by commenters on the subreddit page ELi5.

1. Average global temperature isn’t the local weather outside, nor is it the weather on a particular day (weather is local, climate is global). It is the average weather for the year across the globe. Unfortunately, this obscures the fact that the temperature change is dramatically uneven across the world, making it seem like a relatively mild climate shift. It’s more about the change in extremes which are getting further and further apart. Range of temperatures is getting bigger by just implying a 2 degree average temp change. This also mean bigger temperature and pressure gradients. Scientists use average temperature because if we have to specify extreme temperatures, then time and location will also have to be provided, which is difficult. It is easier to give an average value for laymen terms. Most things can handle 2 degree warmer local weather since that happens every day, sometimes even from morning to afternoon. Many things can’t handle 2 degree warmer average global weather. They are not the same. Here is an XKCD link explaining that the average global temp during the ice age 22,000 years ago (when the earth was frozen over) was just 4 degrees C less than what it is today. The “little ice age” was just ~1-2 degree colder than today. Therefore, each degree in average global temp is substantial. One more explanation is to think about the temperature in your freezer going from 32 to 33F. Still cold, but all the food will spoil. Or the temp difference between frozen ice and liquid water is less than a degree. This means that if the average temperature over an area was below freezing, then with a 2 degree increase, that area is above freezing. We also know that 37 degree F is human body temp, but at 39F, we are ill and 41F is mortal danger. Think about this!
   

   Average Increase in Earth Climate (Source)

2. Earth is a giant thermodynamic engine that takes in energy in higher amounts near the equator where solar gain is greater than heat radiated back in space and funnels it to the poles where solar gain is less than heat radiated to space. CO2 acts like a blanket over the system, taking more heat in. But the fact is, equatorial zones don’t heat much, they just shuttle extra heat to the poles through oceans and wind currents. Same air currents also transfer the CO2 to the poles as can be seen in this NASA model, which further reduces the heat radiated back into space at the poles. This means that the poles are heating up a lot more than 2 degree C, but more like 10 degree C. Resulting melting ice will raise sea levels costing trillions of dollars to either pre-emptively try to deal with or as flood damage. Also ice is the most reflective thing in nature and a large part of our planet is covered in it. This reflects heat back into space. As it melts, it exposes dirt water, the least reflective thing, and it absorbs heat, making the problem worse. Raising temperatures also make permafrost melt which exposes methane pockets that ends up going into the atmosphere. As a result, more permafrost melts and the cycle continues. Methane hydrates also gets sequestered in the ocean and is considered to be a 84 times more potent greenhouse gas than CO2.

Median global sea level rise projections

Population living on land exposed to inundation by 2100  

3. Salty and colder water in oceans near poles is denser which actually forms ocean currents as it migrates to ocean bed and travels to land and so on. With poles melting, fresh water in oceans will lead to the death of ocean currents.
4. Last ice age had a ~5 degree C lower average temp than now and the end of all mammals will be around +6 degree C. On that scale, 2 degree C is quite a movement.
5. Also think about the time it takes to heat up a full pot of water versus a little. Earth is mostly water and if it is heating then it means a large portion of energy is being entered in the system. This does not just heats water but also changes everything else in the ecosystem.
6. CO2 also gets absorbed in the oceans. As rising CO2 levels acidify the oceans, due to the creation of carbonic acid (same acid in soda), organisms with calcium carbonate shells like shellfish and coral grow slower and will likely soon reach the point where their structures will dissolve faster than they grow. This will kick the leg out of the base of the oceans food web and will largely collapse ocean life in near shore areas with the exception of algae and jellyfish. Phytoplanktons are also affected by acidity, and they produce about two thirds of the oxygen we breathe. Intense use of artificial fertilizers makes this problem worse in oceans. Extreme weather changes, coastal cities being flooded, damage to plants, insects, and sea life, and ocean acidity will be the first effects. Mammals can regulate heat better, and humans can adapt. However, the impact on other living beings will imbalance the whole food chain, making species go extinct or struggle to adapt when they otherwise could have manage efficiently. Eventually, it all comes back to humans as we are at the top of the food chain, and will be struggling to maintain our current farming crop yields (as plants would be affected).
7. Our beaches are almost 100% made up of CaCO3. So if oceans become more acidic, then the beaches will also be affected over a period of time.
8. Change in global average (not 2 degree local) can also make some currents very hot but highly populated areas uninhabitable. On the flip side, some currently icy areas can become habitable, though there is no guarantee that they will be fertile. Earth has started to shift out of equilibrium. We are getting high pressure systems that park themselves over an area for weeks. In the ocean, this can kill corals (which is already happening as a result of extreme heat wave). Over land, they reduce crop yields and can kill people. We have a circumpolar band of wind called the polar vortex that will start to meander, bringing snow to Florida and dropping temperatures across the eastern US by 10-15 degree C below normal in the middle of winter for weeks, killing native plants and animals that are not adapted to being able to survive in that cold for long. These shifting weather patterns also change climate in areas such that some areas will see extended drought such that there will no longer be enough water for people. In other areas, heavier rainfall will increase flooding and landslides.
9. As ocean temperature rises, rate of evaporation rises, which provides more fuel for large hurricanes (hurricanes-and-climate-change). It is also because air can hold more water as it gets warmer, so hurricanes, monsoons, and other severe storms get more intense. Water vapour is pretty good at absorbing electromagnetic radiation (70% of all sunlight and 60% of infrared off of earth’s surface), so it is a more intense greenhouse gas. Down the line, they might have less predictable paths, and can affect regions that historically have never seen strong hurricanes.
10. Effects on personal habits of plants and animals are also suggested. Some birds lay only eggs of a particular sex in warmer climates. This might lead to the extinction of another gender. With warmer water in oceans, fish might migrate to different depths of oceans and the birds that feed on them might die hungry. Migration patterns of animals might change. Pollination might be affected. Timing of flowering and pollinating might be off because warmth is a big biological signal for growth change to plants. Some insects might survive more and disrupt the food chain of other interconnected organisms and plants (warmer climate can result in more pathogens). Animals that live in warmer climates are also least adaptable to increase in temperatures. Most of our diversity is in tropical rainforests, so they might face risks. There are temperature limits to survival of proteins as well.
11. At the end, issue is not a 2 degree warmer temperature. It is that 2 degrees could be the tipping point at which it becomes a runaway train effect. Things like melting ice and release of more methane or plants struggling and absorbing less CO2. The two degree difference can quickly become 20 degrees.
12. Another major issue is the timing of this development. It’s not just that climate change is happening, but that instead of happening over a period of thousands of years it is happening in just tens of years. There is no time for life to adapt to the new conditions.
13. Nuclear energy was a good option but oil companies campaigned against it and gave it the bad name that it has today.
14. So life as we know it today is adapted to a particular climate and that is about to be upended. When the dust settles, earth will go on. Humans might not. Earth has been warm before, but not when humans were set up to depend on farming the way we are today. Any time the world goes through a climactic shift, it becomes less habitable to the species that were adapted to old patterns. Because of the interconnected ecosystems, these effects ripple in a positive feedback loop that drives up extinction rates in a runway process that can radically alter the biome. This is not good for humans in the short or long run.