There are a number of concepts that must be understood in order to tune a piano by ear. The following videos teach the basic theory of piano tuning and some of the main terms that are used.
Part 1 - Notes & Intervals
Part 2 - Understanding Partials
Part 3 - What Are Beats?
Part 4 - Coincident Partials
Part 5 - Hertz, Beats and Cents
Part 6 - Temperament
Part 7 - Inharmonicity