Most often, a pool pump will buzz or hum from sitting still over winter, or if the motor capacitor is failing.
Usually, pool pumps contain a cap on the end of the motor that can be popped off, allowing users to manually rotate the motor while the power is off to free up stuck facets from the winter.
When the motor takes longer to start and makes continuous buzzing noises, the capacitor probably needs replacing. If your pump is new, ensure that the correct voltage is being applied to the motor. The voltage will be either 120v or 240v, and the wiring diagram will be displayed on the motor.