'snog' originates from British English slang (early 20th century); exact origin is uncertain and is likely dialectal rather than from a clear root.

'snog' appears in early 20th-century British colloquial usage meaning 'to kiss' and has remained in informal use with essentially the same meaning; 'snogged' is simply the regular past/past-participle form formed by -ed.

Initially it meant 'to kiss or cuddle' and over time it has largely retained that meaning, remaining informal/slang.