My monitor comes with an adapter , which accepts electricity from wall, ranging from 110V-240V. I am wondering how it could output a same amount of current despite a dynamic voltage?
Isolated 220-110 to low voltage supplies are often switch-mode power supplies using a small transformer with a high frequency. If you change the duty cycle of the pwm controlling a power transistor you can change the output voltage. Most switch mode chips have an enable input. The reservoir capacitor on the output can serve as buffer to smooth out the enable and disable cycle.
With some measuring and feedback circuitry (using an opto-isolator to communicate back to the high voltage side) and you can then adjust that duty cycle to emit a constant voltage, a constant current, a current-limited constant voltage or ...
The maximum current would typically be limited by the components selected for the internal regulator circuitry, not by the input voltage or current (since a typical wall socket can supply around 1500 to 2000W, and I doubt your adapter is rated that high). The actual current depends entirely on how much the device it's powering takes.
Typically they rectify to peak voltage AC to DC then DC-DC converter to step down.
There will be using a fixed reference diode voltage to regulate the output.