Really depends on what kind of device you're talking about in particular. If you're talking about an incandescent lamp, then the simplest answer is that incandescent lights are not constant power devices by themselves. An incandescent light is more or less just a resistor, albeit a non-linear one. So, a 12V-rated light attached to a 24V power supply wants to draw about twice the current it is rated for, almost certainly destroying it. This assumes the 24V power supply can supply the additional current.
You suggested powering a 24W light bulb rated for 2A @ 12V. This means the filament is about 6-ohms (once hot). What happens when you attach a 24V supply across a 6-ohm "resistor"? For an ideal voltage source, the current should go to 24V/6-ohms = 4A. But your power supply is only rated for 24V @ 1A.
Two issues:
1. Your power supply is overloaded because the load demands 4A, but it can only supply 1A, so it will probably go into a shut-down protection mode, or it will be damaged.
2. If the power supply could supply 4A, then you'd be running the lamp at 4x the rated power, since 24V * 4A = 96W! That will certainly destroy the lamp
Two ways to drive a 12V lamp with a "24V" power source:
1. Use a constant voltage/constant current (CV/CC) power supply. These power supplies operate in constant voltage mode up until the load draws a predetermined amount of current. As the output current attempts to go beyond this threshold, the power supply counteracts by reducing its output voltage in order to maintain the set-point current. In this case, if you'd need a CV/CC power supply rated for 24V @ 2A. With a 2A set point, the output voltage will be at 12V. Might as well just use a regular 12V power supply.
2. Use PWM to set the average power @ 24W. Since running a 12V lamp @ 24V results in 4x the rated power dissipation, you can run the lamp at 25% (1/4) duty cycle to get the same effective output power. Usually there should be no problem running the filament at a higher voltage (within reason), but would not advise trying to run a 12V lamp at 240V with PWM, for other reasons.