Operational Amplifiers

Op-amps are used to amplify analog signals. By signal it is usually meant voltage, not current. So, op-amps amplify voltage. Their output current is low, on the order of mA.

In a control system, we usually want to drive a high current device like a motor or an electromagnet according to analog sensor (e.g. 49E) readings. Sensors output low voltage values which are amplified by an op-amp. In order to drive high current devices, we feed the op-amp output to a transistor that can handle higher currents. The reason we can't completely replace the op-amp with the transistor is that a transistor usually expects larger voltages at it's base (low current is not a problem) which the sensor cannot provide.

If your sensor output is not analog but digital (e.g. MPU6050 which has I2C output), you have to feed the output to a microcontroller which than can produce a PWM signal fed to the transistor, i.e. there is no op-amp in the digital sensor case.