Capacitors and inductors both are used to store energy in their respecitve ways so that all of that stored energy can be retrieved. To simplfy (I hope):
Capacitors store energy by acquiring a charge called Q for which a capacitance C will yield a voltage V. The relationship between them is Q = C x V for which the stored energy is ½ x C x V².
Inductors store energy by acquiring a current flow I for which the product of voltage V and time T equals the inductance L times the current I. The stored energy in an inductor is ½ x L x I².
In the absense of resistive energy loss, an inductance and a capacitance connected together can transfer some quantity of stored energy back and forth between themselves over and over again. The number of times per second that this happens is called their resonant frequency.
Consider an AC and a DC signal. A DC signal is basically a 0 frequency AC signal. A capacitor blocks a DC component and allows AC to flow. An inductor allows DC to flow and blocks AC. For example a decoupling capacitor will allow any noise to be grounded, while still allowing to DC component to flow. And noise is comprised of many many frequencies. The way a filter works is by allowing certain frequencies to be grounded and allowing certain ones to flow through. the combination of value of inductors, capacitors and resistors determine your cutoff frequency.