What does a transistor do?
Transistors allow you to switch and amplify voltage and/or current. If the motor driver is weak, you may be able to use the motor driver to drive the transistor which will switch the power rail voltage through the motor which may correct your power problems at the motor. A transistor on its own cannot increase voltage or current. It can only lower a voltage/current down to 0 from the maximum. So if your board is driven with a 5V power rail, you cannot get 10V out of it. 

If you're interested in increasing voltage or current, you should look into switch mode power supplies which use either inductors or capacitors with transistors to alter the voltage/current ratio to better serve the load. Note that this doesn't increase power, it only changes voltage to the downside of current or vice/versa.

Also note that amplification of transistors isn't increasing the power of a signal, it's taking a signal and creating a transformed version of it using energy from the power rails.

To answer your question succinctly, a transistor is a switch controlled by another voltage/current.