Since voltage is like water pressure, and current is like the volume of water being pumped, in a given hose (wire), there's a volume threshold based upon its diameter (AWG), but only in relation to the pressure applied (V).
So, if I pour water into a closed end hose, it will fill up and spill out. There is very little or no pressure at all, just gravity.
If I add pressure, I create friction, the hose expands by resisting the pressure (light slowly fades in). Of course, it's a hose, and it has water in it, and therefore it probably won't catch on fire from friction. If I add too much pressure for the hose (AWG) it will burst. If it was a wire, it would heat up and turn into a light saber, which would be great for an oven, or a foam cutter, or a distant galaxy far, far away.
Am I on the right track?
So, the relationship between applied current and burning your house down correlates to the thickness of your wire (whether it's solid or stranded, what material it's made of, etc.,) and the amount of current you apply to that wire.
Where I'm confused is how amperage works. In a hose, or a water line, for example, each outlet valve reduces the volume of water being sent to the next valve until the pressure is reduced to nothing. If we want the pressure to remain constant, we would need to reduce the pipe diameter as the line continues.
In electricity, it seems like it's similar, only the electrical devices draw current, right? Wouldn't that be like adding a pump to the main water line to pump already pressurized water out of the pipe, in which case, if we did, we may deplete the water line too quickly, causing it to collapse.
Is that what's happening when we fire up too many devices that draw more current than the breaker can handle?