When you hear that an input is high-impedance, it means that it accepts little to no current. If an output is high-impedance, it means that it sources or sinks little to no current.
In electronics, high impedance means that a point in a circuit (a node) allows a relatively small amount of current through, per unit of applied voltage at that point. High impedance circuits are low current and potentially high voltage, whereas low impedance circuits are the opposite (low voltage and potentially high current). Numerical definitions of "high impedance" vary by application.
High impedance inputs are preferred on measuring instruments such as voltmeters or oscilloscopes. In audio systems, a high-impedance input may be required for use with devices such as crystal microphones or other devices with high internal impedance.