The DC blocking capabilities of capacitors can be used to remove DC bias from a signal, or to apply a DC bias to a signal. Voltage rating will always given for a capacitor, this is the DC voltage that can be applied before the dielectric material between the capacitor plates will break down and begin to conduct. This means that capacitors actually block DC voltage. There is no direct electrical connection. We can further improve on our understanding by looking at the circuit symbol for a capacitor, or by imagining the mechanical construction. We can see that if frequency reduces to '0', meaning DC, the impedance increases to infinity, as we end up dividing by '0'.
If we use the equation for impedance of a capacitor: As with the passive low pass filter we can see that this capacitor and resistor configuration forms another frequency dependent potential divider allowing higher frequencies to pass more easily and attenuating the lower frequencies, to the point of a complete block of DC signals.