This is a cycle of resistance and capacitance occurring between the input and output of an amplifier circuit, which can create a primitive low-pass filter that is signal dependant. The effective input impedance of an amplifier depends on the impedance connected from input to output of the amplifier. The apparent scaling of this impedance often dominates the input impedance and frequency response of the amplifier. This effect was first reported by John Miller in 1919 and is now commonly known as the Miller Effect or Miller Capacitance.
The term is often seen when reading about guitar amplifier circuit design. It refers to the effective multiplication of the plate-to-grid capacitance in a triode tube (such as a 12AX7) by the gain of the amplifying stage. The same effect occurs in many solid state designs, but we will focus on tubes in this explanation.
A typical triode tube contains a plate, a grid and a cathode. When a tube is amplifying a signal, it has to work against the plate-to-grid capacitance, charging and discharging it as the signal changes. Because the grid is high impedance, and doesn’t draw or source any current of its own, the charging current for it must be sourced or drawn through the driving source resistance of the input stage. This forms a low pass filter, with a cutoff frequency determined by the source resistance/impedance of the previous stage and the input capacitance.
The Miller capacitance in a triode tube is equal to the plate-to-grid capacitance multiplied by a factor equal to the stage gain plus one.