I saw this circuit in an answer to temperature controlled water bath but didn't understand the working and how the temperature would be controlled
I can't teach you how each component works. But I can describe the circuit. This should be sufficient for you to research it further yourself.

The 741 op-amp is being used as a voltage comparator with hysteresis. It is configured to do this by the components on its '+' input: 10 K linear potentiometer, 10 K and 47 K resistors. The exact voltage level it will compare to is set by adjusting the 10 K pot'.

The voltage it compares to comes from a potential divider formed by the thermistor and a 10 K resistor, connected to the op-amp '-' input. As the ambient temperature changes the thermistor's resistance, the voltage from the potential divider to the op-amp '-' changes. When this voltage is lower than the reference voltage from the 10 K pot' circuit, the op-amp output will be its supply voltage, which will turn on the transistor and therefore the relay. When not, the transistor and relay are turned off.

The circuit is missing a clamping diode across the solenoid coil. You can use a 1N4007 diode. Connect the diode anode to the solenoid wire going to ground. Connect the diode cathode to the solenoid wire going to the transistor.

Note that a 200 R resistor is shown in parallel with the pot'. I don't think it should be there. If you build the circuit, try it without this 200 R first.