Servo motors are unique in that they can move to the angle your want and stay there - even when something pushes on it. On the inside there is a closed-loop control system but we can treat the thing as a black box (literally, though they sometimes come in blue.)

There's 2* very distinct flavors of Servo - one for the RC plane/animatronic market and one for high-end industrial automation. There are other nuances like plastic vs metal gearing or analog vs digital circuitry, but they are all controlled in generally the same way.

PROS

• $$ (Hobby-grade) - if you buy direct from China in volume they're not much more than BDCs
• Position shaft easily and stay there
• Control protocol is easy, often doesn't need drivers
• Casing makes them easy to mount
• Lipo-friendly voltages
• Industry-defined standard sizes

CONS

• $$$ (Industrial-grade)
• Not meant for continuous rotation but hacks to exist
• Needs constant signal unlike Steppers

* there is a third flavor sometimes called "Smart" servos that have an on-board MCU but they're a different beast and out of scope for the talk.