This is the 4558th most frequent Russian word.
глубиной
"Глубиной" means "by depth" or "with depth" in English.
In this sentence, 'глубиной' is instrumental case of the noun 'глубина' meaning 'depth', indicating the attribute of the lake.
Озеро поражает своей глубиной.
The lake is striking due to its depth.
Here, 'глубиной' describes the quality of thoughts and is used in instrumental case to express manner.
Он размышлял с глубиной мыслей.
He contemplated with depth of thoughts.
In this sentence, 'глубиной' refers to the concept of feeling, also instrumental case, emphasizing intensity or profoundness.