This is the 4811th most frequent Russian word.
значительный
Significant; considerable; substantial.
Here, 'значительное' describes the degree to which 'влияние' (impact) is significant, indicating importance or magnitude.
Его помощь оказала значительное влияние на успех проекта.
His help had a significant impact on the project's success.
In this sentence, 'значительные' pertains to 'улучшения' (improvements), reflecting the extent or notable degree of the changes achieved.
Мы заметили значительные улучшения после тренировки.
We noticed significant improvements after the training.
In this context, 'значительными' is used to characterize the magnitude of difficulties 'проблемы' (problems) as noteworthy or substantial.