In the Wikipedia page on Islamic views of angels, it's mentioned that they're messengers with wings.
Does Islam offer an explanation for the purpose behind these wings?
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Praise be to Allah, Who created (out of nothing) the heavens and the earth, Who made the angels, messengers with wings,- two, or three, or four (pairs)
— The Holy Quran, Chapter 35 (Fatir), Verse 1
But again from the hadith we can find that Gabriel has 600 wings:
Narrated Abu Ishaq-Ash-Shaibani: I asked Zir bin Hubaish regarding the Statement of Allah: "And was at a distance Of but two bow-lengths Or (even) nearer; So did (Allah) convey The Inspiration to His slave (Gabriel) and then he (Gabriel) Conveyed (that to Muhammad). (53.9-10) On that, Zir said, "Ibn Mas'ud informed us that the Prophet had seen Gabriel having 600 wings." —Muhammad al-Bukhari, Sahih al-Bukhari, Volume 4, Book 54, Number 455
So the crux of the matter we can find from the same verse of 35:1
He increases in creation what He wills. Indeed, Allah is over all things competent. (35:1)
It doesn't matter that how many wings they have or why they have wings but what matter is Allah has set some examples for us to understand his greatness, knowledge,power whatever.