Schmitt triggers switch an output based on 2 threshold voltages that are spaced apart so that there is is range (hysteresis), where the output stays in the last condition it was put into. For the 555 timer, this is typically between 1/3 and 2/3 of the supply voltage. Inverter means that the input has to go high (above 2/3Vcc) for the output to go low. Whereas the input has to be low (below 1/3Vcc) for the output to go high.
Other basic 555 timer circuits
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