A strain gauge is a strain dependent resistance, consisting of a thin foil. Strain gauges are usually used to measure deformations of objects they are glued to. When the foil of the strain gauge is deformed, its electrical resistance changes.
Caution: temperature changes can also affect the resistance of the foil.
Strain gauges are normally applied in a so-called Wheatstone bridge configuration. In a bridge of Wheatstone, temperature compensation can be incorporated using a dummy gauge. Keep the voltage on the bridge low to prevent heating of the strain gauge. Since the signals of a strain gauge are usually in the mV range, you will need to amplify them to be able to read them using a microcontroller.