"If a certain switch box is then rated at only 100 watts because it basically has thin wire/contacts/circuitboard on the inside, what happens if you then have a 300 watt amp that you are driving very loudly through it?"
I assume you mean that the amp is trying to put more than 100 watts through the switch. If the power exceeds 100 watts only on brief peaks, probably nothing happens. If the power exceeds 100 watts only slightly but for longer periods, say a few seconds or more, probably nothing happens since the switch would typically be rated conservatively. If the power exceeds 100 watts by a lot and lasts for longer periods, then something in the switch will likely melt. When a circuit element is forced to pass more current than its design, it tends to heat up and eventually to melt. This is how fuses work to limit current in a circuit. There may be audible deterioration in the sound quality (briefly) before it melts due to the current limiting aspect of an overheated circuit element. Depending on the circuit element and the extent of over driving, there could be ancillary damage to surrounding elements, including a fire.
I assume you mean that the amp is trying to put more than 100 watts through the switch. If the power exceeds 100 watts only on brief peaks, probably nothing happens. If the power exceeds 100 watts only slightly but for longer periods, say a few seconds or more, probably nothing happens since the switch would typically be rated conservatively. If the power exceeds 100 watts by a lot and lasts for longer periods, then something in the switch will likely melt. When a circuit element is forced to pass more current than its design, it tends to heat up and eventually to melt. This is how fuses work to limit current in a circuit. There may be audible deterioration in the sound quality (briefly) before it melts due to the current limiting aspect of an overheated circuit element. Depending on the circuit element and the extent of over driving, there could be ancillary damage to surrounding elements, including a fire.