An adverbial phrase meaning 'to an unbelievable degree' or 'so ... that it's hard to believe', emphasizing an extreme extent.
ありえないほど高いビルが夜空にそびえていた。
An unbelievably tall building towered into the night sky.
彼の走るスピードはありえないほど速い。
His running speed is unbelievably fast.
ありえないほどの量の注文が来て、店はてんてこ舞いだった。
An unbelievable number of orders came in and the shop was swamped.