Latin, tercius denarius.
The third penny was one-third of the profits of justice in a Hundred or shire. In most cases, the third went to the king, sometimes to the earl, occasionally to another magnate. The 'third penny' from a borough was different. Boroughs normally paid an annual levy to the king; but on occasions the borough revenues were divided between the king and the earl (or sometimes the sheriff), the king receiving two-thirds, the earl or sheriff the 'third penny'.
See J.H. Round, 'The third penny', English Historical Review, vol. 34 (1919), pages 62-64.