The first Cmos Schmitt-trigger gate is an inverter oscillator so that the probes are fed with AC to avoid plating on them which would happen with a DC signal.
The second and third gates produce a pulse-width-modulation output determined by the resistance (wetness) of the soil.
The 47k resistor and 22uF capacitor smooth the PWM waveform into a variable voltage.
the 4th gate triggers the transistor when the voltage drops to its Schmitt-trigger voltage level.
The transistor drives the relay for the watering pump.
The LM3914 is a voltmeter that shows the filtered variable DC voltage which shows the wetness of the soil.