What is electromotive force and how is it different to potential difference?

The electromotive force or emf of a cell in a circuit is, for a start, not a force at all: it has the unit of volts. A good definition is ‘the power supplied by the cell per unit current through the cell’ or, equivalently, ‘the energy supplied by the cell per unit charge through the cell’ (IB examiners love to ask for this by the way). When the internal resistance of a cell is zero (or negligible), the emf is exactly the same as the potential difference (or voltage) between the terminals of the cell. But this changes when the internal resistance is significant – this is the resistance inside the actual cell which will ‘use up’ some of the emf before the current even leaves the cell. Since V = IR, you can find the potential difference across this internal resistance by multiplying the resistance by the current through it. Taking away this value from the emf will give you the remaining potential difference between terminals of the cell.