Schmitt Trigger Oscillator - How does it work?
The schmitt trigger inverter is what generates the signal that charges and discharges the capacitor. Assume the input on the left starts at 0V; the schmitt inverter will therefore output +5V. This +5V will charge Ct via Rt until the voltage crosses the schmitt trigger's rising voltage threshold. At that point, the output will change to low, and start discharging the same capacitor until the schmitt trigger's falling voltage threshold is crossed, starting the cycle over again.

Power for the schmitt trigger's output voltage comes from its power supply - marked +5V in the diagram.