Why there are minimum three electrodes used in ECG, EMG measurements?
In fact, two is enough. Try putting an electrode to each hand. Yet, some ECG input stages have almost literally infinite input resistance. So just two electrodes may (and actually do) float away out of the input range. So here comes the third electrode, that puts the whole body potential somewhere near the 0V of the input. 

By the way, the high input resistance is required to maintain best possible CMRR, which is mandatory for good ECG reading. 

Edit

Oh, i forgot another, even more common usage! Poor me... Thee is a feature called RLD. Similar to the reference i mentioned, but instead 0V it applies opposite of common mode from the two electrodes. That almost cancels the common mode, and again, improves CMRR.