It depends upon the nature of the appliance but generally speaking if the voltage is too high it draws too much current and burns out, if the voltage is too low it draws too little current and/or does not perform to its rating. The mathematical reference is Ohm's Law and the Power Triangle.
If you plug an 110V appliance in 220V outlet (same as 120v to 230v, 240v) you can only hope that some protection device disconnects the power to the appliance.
If it is some kind of heating device, (toaster, incandescent light, space heater) it will develop close to four times the designed heat, and probably burn out in minutes, or seconds. If it is some AC drive, it most likely will burn out very quickly. If it is a universal drive, (or DC), it may spin up to twice its intended speed, and wear out quickly.
If you plug a 220V device into 110V outlet, it will normally last a little longer before it dies.
An AC mechanical drive may fail to start, or it may take up more current than it is designed for, and eventually burn out.
The insulation is usually not a problem unless there is a major flaw in the design. It is current that is your enemy, a piece wire that is warm at 110V (120v) will turn into a fuse at 220V (230v, 240v), all other things being equal. Determining the wattage/load is usually performed by the design engineer to meet the performance specs set by the electrical engineer.
In all cases, you are probably contravening local regulations, because in most countries, the electrical sockets are designed to accept only certain plugs, in order that you do not mismatch appliance voltage and outlet voltage. In some countries, you can get severely punished if anything goes wrong because you tried this.
You can simply buy a 110v to 220v converter to make the appliance works smoothly.