It implies that the thing being produced is:

* Unlikely: It seems impossible to have been created under the circumstances.

* Unprepared for: There was no evidence or preparation for its appearance.

* Perhaps even imagined: The origin of the idea might be unclear or even nonexistent.

Here are some examples:

* "The politician pulled a solution out of thin air to solve the economic crisis, but it lacked any real practicality."

* "She managed to pull a fantastic dinner out of thin air, despite having no ingredients in the fridge."

* "The comedian pulled a series of jokes out of thin air, keeping the audience entertained."

The phrase emphasizes the unexpected and often miraculous nature of something appearing from nowhere.