Say you have a fresh capacitor that has never been in a circuit. When a voltage is applied across the capacitor's terminals, current will flow into one of the capacitor's plates, creating a build up of charge, and flow out of the other plate, creating a negative charge.
Once the current from Capacitor stops, magnetic field of Inductor collapses enabling the current to flow through the circuit. This current reaches the Capacitor and charges it again building charges in its plates and develops voltage across it. This cycle continues to repeat over and over again generating signals of resonant frequency.
The key thing to understand here about timing circuits is that capacitors appear as though they are short circuit while they are charging, but as soon as they are charged, they appear to be open circuit. If you pass DC through a capacitor, it will charge and then block any further current from flowing.
Current flowing in Capacitor when AC is applied tend to lead the voltage by 90°. Take a look at the below graph. Consider AC voltage is applied across a Capacitor, initial voltage will be minimum and at this instant charging current will be at maximum as you can see in the above graph.
If you have unwanted DC voltage (low frequency), it will block the DC signal and only allow the AC/RF (high frequency) to go through. So, if you have an AC signal, you can put a series capacitor to make sure no DC goes through and hurts the rest of your circuit. Inductor:
The flow of charging current keeps charging the Capacitor until the voltage developed equals voltage applied across it. At this point the charging current ceases to flow due to the developed voltage across Capacitor. In this instance Capacitor is fully charged with Positive charge in one plate and equivalent Negative charge exists in another.