This is the 4734th most frequent Polish word.
niezmiernie
Extremely; immensely.
Here, 'niezmiernie' intensifies the adjective 'wdzięczny' (grateful), emphasizing the high degree of gratitude experienced.
Jestem niezmiernie wdzięczny za twoją pomoc.
I am extremely grateful for your help.
In this sentence, 'niezmiernie' enhances 'piękny' (beautiful), emphasizing the extraordinary beauty observed.
Widok góry był niezmiernie piękny.
The view of the mountain was extraordinarily beautiful.
'Niezmiernie' here modifies 'ważna' (important), indicating a significant level of importance perceived.