What is the meaning of this statement “Allah does whatever He wills”?
The meaning of: “Allah does whatever He wills” is that Allah has the Power to bring into existence whatever He eternally willed to exist. Nothing makes Allah powerless from doing that, and no one prevents Him from doing it, nor does He need assistance from others. Allah said in Surat al-Baqarah verse #253:
﴿ولو شاء الله ما اقتتلوا ولكنّ الله يفعل ما يريد﴾ سورة البقرة
This verse means: [And if Allah had so willed it, they would not have fought one with another, but Allah does what He will].
Allah said in Surat Hud verse # 107:
﴿إنّ ربّك فعّال لما يريد﴾ سورة هود
This verse means: [Allah does whatever He willed.]