As noted, using 220 cuts the current in half which reduces the losses in the wire. Furthermore, as a percentage of the voltage, since the voltage has doubled and the current has halved, the drop in the line is only 1/4th as much percentage wise.
To put into numbers, say you were running 110 and required 10 amps of current. If the wire resistance was 2 ohms, the voltage drop in the line would be 20 volts (amps x resistance). That's a 20% (roughly) voltage drop and likely to be too low for the motor. However, if you run 220 with the same wire, the current is only 5 amps and the voltage drop in the line is 10 volts (amps x resistance). Now you are getting 210 volts at the motor, which is only a 5% drop and is acceptable.
Ken