It is basically a GATE and can be used as an INVERTER. But the Schmitt Trigger input gives it a lot more features.
The Schmitt Trigger Inverter is shown on the left and the Schmitt symbol must be included to show it is not an ordinary inverter.
It can be used as an Inverter, an oscillator, a Buffer as well as other "Building Blocks." It all depends on the surrounding components.
HOW THE SCHMITT OSCILLATOR WORKS?
Suppose the input is LOW. The output will be HIGH. The voltage across the resistor will cause current to flow through it and charge the capacitor. When the voltage on the capacitor reaches 67% of rail voltage, the gate will change state.
The energy in the capacitor will "bleed" through the resistor and the voltage across the capacitor will gradually fall. When it reaches 32% of rail voltage, the gate will change state.