This is the 16171st most frequent Polish word.
ulgą
"Ulgą" means "relief" in English.
The word 'ulgą' is used as an instrumental case form of 'ulga' (relief) to describe the means by which relief is experienced—here, it is indicated that the relief is provided by 'jego słowa' ('his words').
Jego słowa przyniosły mi wielką ulgę.
His words brought me great relief.
'Ulgą' is in the instrumental case and is used as a modifier describing the manner ('z ulgą' - 'with relief') in which she accepted the news.
Z ulgą przyjęła wiadomość o jego powrocie do zdrowia.
With relief, she accepted the news of his recovery.
In this sentence, 'ulgą' is used in a similar instrumental case construction 'z ulgą' to describe the manner ('with relief') of his actions.