When Gandalf gets stuck in Sarumans tower a Butterfly/Moth comes to visit him and appears to prepare him that something is about to happen. In this case a Giant Eagle comes and saves him, Is there an explanation to this? Does Gandalf give the moth a message to send to the Eagles? Can anyone elaborate on this ?
The moth just exists in the movies, but a possible source in the books is in Gandalf's parting words to Radagast, as relayed by him at The Council of Elrond:
The moth could therefore be one of "the beasts and birds that are your friends" (although the movie omits the Radagast scene).
Of course in the books the Great Eagle comes directly to Orthanc and there is no indication that he was summoned or conjured from a moth in any way:
The moth also appears in the movies during the "Black Gate Opens" scene, where again it presages the Eagles, and likewise in the first Hobbit movie (we can expect the same in the third).
Beyond that there is no indication of what, if any, significance it has other than just being a movie conceit.
In the movie, the moth is just a moth who happened to pass by, and Gandalf deftly captures it (he must have trained with that guy). Then Gandalf "talks" to the moth and releases it. Apparently, Gandalf is a master hypnotist and convinces the moth to transmit a message to the eagles. He does the same again in the Hobbit movie. In the books there is no moth; it is a movie-only element.
You have to admire the moth, though:
The Great Eagles are the servants of Manwë
Gandalf is a member of the Isarti - along with Saruman and Radagast - sent by the Valar to aid the inhabitants of Middle Earth against Sauron.
In both appearances of the moth in the Peter Jackson movies, it appears to Gandalf just before before the eagles appear. My interpretation is that the moth is a messenger to Gandalf from Manwë sent to inform him of the imminent arrival of the eagles.
The the novel, Gandalf also receives the direct aid of the Valar when he dies after defeating the Balrog. His spirit is 'sent back for a while', presumably to Valinor, before he is resurrected as Gandalf the White.