Consider the conceptual circuit shown below of a thevenin equivalent source driving the equivalent circuit of an amplifier. Rin is the input resistance, A is the voltage gain and Rout is the output resistance.
simulate this circuit – Schematic created using CircuitLab
Note that the source impedance R2 forms a voltage divider with the input resistance. This means that the higher Rin, is the more of the source voltage will be dropped across it and therefore amplified. The smaller Rin is the more voltage would be dropped across the source impedance, we call this effect loading.
A high input impedance means it will also draw a negligible current, which is one of the golden rules for Op-Amp analysis as mentioned in the answer below.