Matching appropiate current value for components
Most products and many components such as ICs are designed to operate from a constant voltage supply. They will draw what current they need, provided the voltage is in the correct range. 

A device that is supplied with a 19V 5A adapter will operate properly from a 19V 100A power supply (assuming it meets any other requirements) and will draw no more than 5A. It may not operate properly from a 19V 4A supply. It may not operate properly from a 15V 10A supply or a 24V 5A supply (and either case could damage it). 

LEDs are designed to operate at a certain current, not voltage. An external circuit (maybe just a resistor) is typically used to allow them to operate from a constant voltage. If you supply more than the rated current to an LED you may well damage it. It may get brighter, to some extent until internal heating and damage reduce the brightness, permanently if you go too far. 

The analogous case with LEDs is that if you supply an LED from a constant-current supply of (say) 15mA it will take the voltage it needs. That might be 3.1V for a white LED or 1.9V for a red LED. The fact the constant-current supply is capable of 3.5V or 350V won't change the LED voltage.