A treadmill's motor powers the track. Treadmill motor power is described in terms of horsepower (HP), and you specifically want to know continuous horsepower (CHP). CHP is most useful because it indicates how much power a motor can put out continuously versus just at its peak. Treadmill motors vary from a very low 1.5 CHP to full commercial machines with 5.0 CHP motors.
How much treadmill motor power do you need? That depends on your type of exercise and your body weight. For people weighing up to 200 pounds, here are general recommendations:
If you weigh more than 200 pounds, then add another 0.5 CHP.
More info at https://www.treadmillreviews.net/treadmill-buyers-guide/
The following is adapted from http://www.thurmansbikeandsport.com/wp-content/uploads/2011/01/treadmill-reasons.pdf
4 HP does not necessarily mean 4 CHP.
You really want to know the continuous HP or CHP rating. CHP means that the motor will run at that given horsepower indefinitely without burning up the motor. In other words, if you get a treadmill with a motor rated at 4 CHP it will provide 4 HP for many years without damage to the motor.
Many treadmill sellers trick consumers by either listing the peak horsepower of the motor or just "HP" which in effect is the peak horsepower rating. Peak horsepower is the highest generated horsepower that can be produced by the motor but the difference is that peak horsepower can only be maintained for a short period of time before the motor starts to burn up. You can find peak horsepower ratings listed on lower priced treadmills ranging from 2.5 to 4.0 HP. In reality, the continuous duty rating of these motors is in the 1.25 to 2.0 range. Such low CHP ratings are well below what you want for a positive treadmill experience.
The more CHP, the faster the belt will speed up and slow down and the smoother your workout will be. A 2 CHP treadmill may take over 60 seconds to speed up from a 3 mph walk to a 7 mph run. Conversely, a 4 CHP treadmill will accomplish such a change in belt speed in 16 seconds.