the transistor is a device that consumes power.
it has a gain. the TIP120 is listed as 1,000
a smaller switching transistor might be 150.
this is a ratio.
for the TIP120 you need to feed it power, you feed it 1 amp and it will allow 1000 amps to pass...
since your device is 1 amp, you need to feed it 1/1000 of one amp.
but..... since the opto consumes a tiny bit of power, you will not get 12.000 volts and the resistor will consume some, so you will not pass power without some changes. you might get 9 volts....
part of the calculations are to allow for the actual values at the pins.
the load will consume some power and the TIP120 has a resistance that will also have some effect.
the bottom line is that you have to feed the TIP120 some current and it will drain that to ground, and while it is draining to ground it opens the gate for the larger current from the collector.
in the TIP120 the ratio is 1000:1 you supply 1 and you allow 1,000 of the other to pass.
the calculations are to allow for all the voltage drops, resistance, etc.