This is the 7724th most frequent Russian word.
значительная
Significant.
The word 'значительное' is here used as an adjective modifying the noun 'влияние', demonstrating the concept of being substantive or impactful.
Эта статья оказала значительное влияние на общество.
This article had a significant impact on society.
The word 'значительное' is used here as an adjective modifying 'число', describing the quantity as large or noteworthy.
В этой коллекции значительное число произведений искусства.
This collection contains a considerable number of artworks.
The word 'значительных' is the genitive plural form of 'значительный', agreeing with 'успехов', and it describes the nature of the achievements as notable or impactful.