Principal English Translation:
1) that, that one, a pronoun that demonstrates (see Lockhart)
2) directional particle meaning "away" or "at a distance" (see Molina)
Alonso de Molina:
on. es particula que se junta a verbos para significar distancia de lugar, o por via, o manera de ornato y buen sonido.
Alonso de Molina, Vocabulario en lengua castellana y mexicana y mexicana y castellana, 1571, part 2, Nahuatl to Spanish, f. 77r. col. 1. Thanks to Joe Campbell for providing the transcription.
Lockhart’s Nahuatl as Written:
demonstrative pronoun. 228
James Lockhart, Nahuatl as Written: Lessons in Older Written Nahuatl, with Copious Examples and Texts (Stanford: Stanford University Press and UCLA Latin American Studies, 2001), 228.
Attestations from sources in English:
The directional particle on can also relate to time, as in thinking forward into the future. The other directional, hual, too, can express a sense of time, as in "back into time."
Also, "in some dialects" the expression on "represents a reverential (derived from the idea of distance)."
Rebecca Horn's notes from Nahuatl classes with James Lockhart at UCLA. Card file in the possession of Stephanie Wood.