Skipping school or avoiding responsibility by sneaking away or hiding.
Possibly from Dutch 'bonk' (a sleeping place aboard ship); students would hide in bunk-like spaces to avoid school, or from a word meaning to jump or leap away.
The exact origin is mysterious, but 'bunking off' became especially popular slang in British English, where it perfectly captures the feeling of skipping school as sneaking away.
Complete word intelligence in one call. Free tier — 50 lookups/day.