Average annual temperatures can change just slightly and have drastic consequences. The 2 degrees you mention are what we're trying to drastically avoid for global climate change (though we won't). It's also believed that a volcanic eruption in the mid 6th century CE lowered global temperatures by 2 degrees for several years, leading to the collapse of several civilisations around the world, and a really bad time in most others. Those 2 degrees are also the difference between London and Bordeaux. So yeah, while a single day being 2 degrees warmer or colder might not feel that different, changing average temperatures by 2 degrees is a massive difference.