adverb
piled up high; in a heap
Describes things stacked or accumulated to a great height, often with a sense of disorder or abundance.
See also: 堆い
机の上に書類がうず高く積まれている。
Documents are piled up high on the desk.
落ち葉がうず高く積もっていた。
Fallen leaves had piled up in a heap.
堆い is the adjective form meaning 'piled up high' or 'heaped', while うず高く is the adverbial form.
The exact derivation is uncertain; the word is conventionally associated with the kanji 堆, meaning 'heap' or 'pile'.