You mean, as opposed to welding machines which are "constant current" design, which are used for SMAW aka "stick welding."
In MIG welding, using constant voltage is critical to arc stability, as it controls the arc length and the wire melt-off rate. Without the constant voltage, smooth arc operation and smooth metal transfer would be impossible. This was discovered early on in the development of MIG welding in the 1950's
The logic rule of MIG welding, is the wire feed speed affects the current, and the heat input in the weld, while the voltage controls the arc length and the arc stability.
To understand why this is, you need to know a little about the physics of electricity, namely "Ohm's Law":
Voltage = Current x Resistance,
and "Joule's Law"
Power = Current x Voltage
Now, the resistance of an electrical arc depends on it's length, just like the resistance in a wire will increase, the longer the wire is. //Increasing the arc length will increase the resistance!//
So, according to Ohm's Law, if the voltage is always the same, then increasing the resistance will decrease the current. Therefore, according to Joule's Law, if the voltage is the same, then a decrease in current will cause the total power of the arc to decrease, and hence the heat of the arc will be reduced
In summary, with a constant voltage welding machine, increasing the arc length decreases decreases heat input. (This is in contrast to a "constant current" machine used for stick welding, where increasing the arc length, to a certain extent, increases the heat input.)
Why is this fact important to MIG welding? Since the wire is being fed into the weld at a constant speed, if the arc gets too long, the reduction in heat input will cause the melting-off rate to slow, until the end of the wire moves closer to the weld, and the heat input increases again.
When you first press the trigger, This constant "feedback cycle" of the wire melting off, versus the arc getting longer and colder, works to stabilize the arc in less than a second. Eventually this causes the arc length to reach a size where the melt-off rate equals the wire feed speed.
Hope that makes sense.