What is the role of each component in the circuit?

Resistors limit currents in a circuit to a precise degree and control voltages within the circuit.
Capacitors can store electrical charge and if coupled to a resistor giving timing functions. Capacitors block dc currents and act as coupling devices for ac signals.
Transistors act as gain blocks that can amplify signals and actively respond to changing circuit conditions.
Inductors or coils can act as frequency filters,generators or energy storage devices. Two coils wound on a common core are called Transformers. These can step up and down voltages and isolate sections of a circuit from other parts.
Diodes can rectify ac signals and block dc current as required.
Integrated circuits contain all the above components in miniature