I heared a rumour that some of the Ainur (Valar and Maiar) are described as brothers or sisters. Where in Tolkien's writings or letters does it happen? What is its meaning?
See also Were all Ainur made at the Beginning? which asks whether some Ainur are children of other Ainur.
From the published Silmarillion:
But Manwë was the brother of Melkor in the mind of Ilúvatar, and he was the chief instrument of the second theme that Ilúvatar had raised up against the discord of Melkor; and he called unto himself many spirits both greater and less, and they came down into the fields of Arda and aided Manwë, lest Melkor should hinder the fulfilment of their labour for ever, and Earth should wither ere it flowered. (AINULINDALË)
Mightier than Estë is Nienna, sister of the Fëanturi; she dwells alone. (VALAQUENTA)
His spouse is Nessa, the sister of Oromë, and she also is lithe and fleetfooted. (VALAQUENTA)
The spouse of Oromë is Vána, the Ever-young; she is the younger sister of Yavanna. (VALAQUENTA)
And it is sung that in that feast of the Spring of Arda Tulkas espoused Nessa the sister of Oromë, and she danced before the Valar upon the green grass of Almaren. (VALAQUENTA)
According to Tolkien Gateway:
The Ainur were the "offspring of Ilúvatar's thought", and each was given understanding only of that part of the mind of Ilúvatar from which they came. The exception to this was Melkor, the greatest of the Ainur, who had a part of the gifts of all the others.
Although all Ainur are made of the thought of Ilúvatar, in His mind some were siblings.
In The Silmarillion, "Ainulindalë: The Music of the Ainur", we have the following quote to back this up (emphasis mine):
But Manwë was the brother of Melkor in the mind of Ilúvatar, and he was the chief instrument of the second Theme that Ilúvatar had raised up against the discord of Melkor; and he called unto himself many spirits both greater and less, and they came down into the fields of Arda and aided Manwë, lest Melkor should hinder the fulfilment of their labour for ever, and Earth should wither ere it flowered.
Tolkien explains this further in one of his letters (Tolkien's Letters, Letter 211; emphasis mine):
In the cosmogonic myth Manwë is said to be 'brother' of Melkor, that is they were coëval and equipotent in the mind of the Creator.
Interestingly, some references to siblings were edited out of the Ainulindalë. The original text read (emphasis mine):
And Manwë and Ulmo and Aulë were as Kings; but Varda was the Queen of the Valar, and the spouse of Manwë, and her beauty was high and terrible and of great reverence. Yavanna was her sister, and Yavanna espoused Aulë; but Nienna dwells alone, even as does Ulmo. And these with Melkor are the Seven Great Ones of the Kingdom of Arda.
but this was edited by Christopher Tolkien because in a later account of the Valaquenta Yavanna was not Varda's sister, and the conception of the Seven Great Ones was changed. The published version says that among the Valar:
Nine were of chief power and reverence; but one is removed from their number, and Eight remain, the Aratar, the High Ones of Arda: Manwë and Varda, Ulmo, Yavanna and Aulë, Mandos, Nienna, and Oromë.
