What is the use of transistor in water level indicator?

It is used to amplify the current. The common-emiiter amplifier is designed so that a small change in voltage (Vin) changes the small current through the base of the transistor; the transistor's current amplification combined with the properties of the circuit mean that small swings in Vin produce large changes in Vout. Various configurations of single transistor amplifier are possible, with some providing current gain, some voltage gain, and some both.