The story
From military time, in which hours before 10:00 am are prefixed with a zero, read as "oh", and 00 minutes is read as "hundred", as in oh five-hundred for 5:00 am.
Etymology from Wiktionary, CC BY-SA 4.0.
oh dark hundred
Today it means: Some unspecified hour in the early morning (implies an unpleasant time to be awake) Full definition →