[Esel Mann]

A (typical hobbyist/RC) servo contains two (electrical) elements within its enclosure. The motor, and the positioning circuitry. BOTH utilize the same power source and BOTH utilize the same ground. Hence the common 3-terminal interconnect from the servo is made up of: power, ground, and PWM control signal input (referenced to the mentioned ground).

In order for your MCU board to provide a control signal to the servo, which the servo can "interpret", 2 key criteria must be satisfied.
First the (voltage based) digital logic level of the control output from the MCU board must be compatible with the (voltage based) digital logic level of the control input into the servo. Second, the ground reference for both must be the same (presumption: no isolation circuitry on the servo outputs at the MCU board). The digital logic levels are always in reference to the associated ground. Hence the grounds being shared permit the logic level from the output side (the MCU board) to be correctly "interpreted" by the input side (the servo).