"Out of the blue" is an informal English

English language

English is a West Germanic language that arose in the Anglo-Saxon kingdoms of England and spread into what was to become south-east Scotland under the influence of the Anglian medieval kingdom of Northumbria...

 idiom

Idiom

Idiom is an expression, word, or phrase that has a figurative meaning that is comprehended in regard to a common use of that expression that is separate from the literal meaning or definition of the words of which it is made...

 that describes an event that occurs unexpectedly, without any warning or preparation.Pocket English Idioms: "Out Of The Blue" from GoEnglish.com It is used as an adverb

Adverb

An adverb is a part of speech that modifies verbs or any part of speech other than a noun . Adverbs can modify verbs, adjectives , clauses, sentences, and other adverbs....

. The "blue" in the phrase refers to the sky

Sky

The sky is the part of the atmosphere or outer space visible from the surface of any astronomical object. It is difficult to define precisely for several reasons. During daylight, the sky of Earth has the appearance of a pale blue surface because the air scatters the sunlight. The sky is sometimes...

, one from which a sudden thunderstorm

Thunderstorm

A thunderstorm, also known as an electrical storm, a lightning storm, thundershower or simply a storm is a form of weather characterized by the presence of lightning and its acoustic effect on the Earth's atmosphere known as thunder. The meteorologically assigned cloud type associated with the...

 is unexpected.

For example, if a father suddenly perishes in an accident

Accident

An accident or mishap is an unforeseen and unplanned event or circumstance, often with lack of intention or necessity. It implies a generally negative outcome which may have been avoided or prevented had circumstances leading up to the accident been recognized, and acted upon, prior to its...

and his daughter inherits an unexpected fortune, then the money came to her "out of the blue."

Longer and more explicit variations include out of the clear blue sky and out of a clear blue sky.