I'm no expert, but this is my understanding...
Higher temperature causes more evaporation from the oceans (which, as everyone knows, cover 3/4 of Earth's surface). This evaporation may be minute in small areas, but when it happens across huge oceans the total effect is... noticeable. After all, that's how storm clouds form over the oceans. And the oceans are vast, and little bits of extra evaporation over vast areas amass to noticeably greater clouds. So a slight increase in temperature over vast areas cause greater storms. These storms might have happened even if global temp stayed low, but with higher temperatures the storms become more violent.
Now, if a winter temperature "ought to have been" -10C, then the clouds will freeze and fall as snow. If the temperature increases to -9.3C, then the clouds will still freeze and fall as snow, but... because the evaporation over the oceans was greater (water evaporates even when very cold), the clouds will hold more water, leading to more snow falling.
All these weather events lead to greater hurricanes, greater floods, greater snowfall, etc. All these are costly to humans, and often more so to fragile eco-systems.
As to why dry areas are expected to become drier, I don't know. Hope someone else can enlighten us on that.
2. Aggravating factors
There are large swathes of tundra across northern Asia that is mostly frozen. And if that melts (and some of it already is), then we'll have more fertile land to live on, except... that tundra contains lots of rotting vegetation that, when thawed, releases lots of methane. Methane is a much more potent greenhouse gas than CO2. Luckily methane decomposes after some years, presumably by being combusted into H2O and CO2, thereby still being an unnecessary addition of greenhouse gas.
The arctic ice can be thought of as a thermostat. In the winter it freezes and grows. One could think of it as "storing cold" (although that idea makes about as much sense as "centrifugal force"). When the summer heat thaws the antarctic ice, cold waters are released which cool the northern hemisphere, thereby evening out summer and winter temperatures. But, global warming causes the freezing zone to shrink. I wonder what will happen the summer when there is not enough ice to even out the summer warmth.
As you say, it is a minor fluctuation. But the problem is, as you also say, the average global temperature, and it's that which makes all the difference.
Anyone more knowledgeable willing to weigh in?