1
general::
At every hour exactly; one o'clock, two o'clock, and so on. For example, The shuttle to New York departs on the hour. An extension of this idiom is every hour on the hour, meaning every time the clock's big hand reaches twelve, as in The bus passes by the house every hour on the hour.
American Heritage Idioms
2
general::
Phrase(s): on the hour
at each hour on the hour mark. • I have to take this medicine every hour on the hour. • I expect to see you there on the hour, not one minute before and not one minute after.
McGrawhill's American Idioms And Phrasal Verbs