As a Verb or Adjective:
1. To happen exactly at the time arranged. English = (be) punctual. Idiomatic English = (be) on time.
2. To happen exactly on the hour.
As Modifier:
1. Used immediately next to a time sign specifying a particular time (6 o'clock, 9 o'clock, etc.) to mean that time exactly. English = precisely. Idiomatic English = on the dot.
2. Used immediately next to a verb to mean the action takes place exactly at the time it is meant to, usually on the hour. English = punctually.