Resistance and Impedance
Impedance is a more general term for resistance that also includes reactance. In other words, resistance is the opposition to a steady electric current. Pure resistance does not change with frequency.
Reactance, however, is a measure of the type of opposition to alternating current electricity due to capacitance or inductance. This opposition varies with frequency. Impedance is the total contribution of both resistance and reactance. This is important for alternating current analysis and design. At direct current, reactive elements can be replaced with their steady-state model and resistance can be considered.
Often you'll hear about the impedance of transmission lines, like the cables which run between components of your stereo system, and impedance of things like speakers. You'll also hear that it is important to match these or else you'll get reflection.
Note that impedance and reactance are both given in units of 'ohms' just like resistance. Capacitance is measured in Farads and inductance in Henries, and these relate to impedance, but they are not measures of impedance.