Volts are what the wall pushes, amps are what the device draws. The device will attempt to pull as many amps as it can/needs. The wiring in your walls can only handle so much amp draw before overheating and melting. It would be possible to install thicker wires that handle more amps, but that would be expensive and unnecessary.

Your breakers have specific amp limits, usually 15 or 20. If a device (or several devices on the same circuit) try to pull more than the rating of the breaker, the breaker trips and cuts power, preventing the wiring from melting and starting a fire. A fuse does the same thing, except a fuse has a piece of wire that is supposed to overheat and melt at a specific amperage which again cuts power and protects everything else.

Some circuits in your house will have more expensive, thicker wiring and a higher amp breaker for devices that need it - like your dryer or water heater.

The vast majority of North American homes will be primarily 15 amp circuits/breakers, with a couple higher amp breakers for, like, your kitchen (for the microwave and electric stove and whatnot), and then a couple dual-phase 240v circuits and/or with 30 amp breakers. You might also see a 30 amp breaker elsewhere, like a garage, maybe if you have an electric outdoor heater, but that 30 amp circuit will have thicker, more expensive wiring.