na-adjective, noun which may take the genitive case particle 'no', noun
unexpected; unsuspected
Describes something that was not anticipated or thought of; often used for surprising events, outcomes, or facts.
I was surprised by the unexpected result.
Everyone was puzzled by his unexpected behavior.
予想外 emphasizes that something was outside of predictions or forecasts, while 意想外 can also mean 'unsuspected' or 'not even thought of'.
Compound of 意想 (isō, 'thought; expectation') + 外 (gai, 'outside'). The exact historical derivation is uncertain, but the word is conventionally associated with the meaning 'outside of what one thought'.