This is the 1713th most frequent Russian word.
влияют
"Influence" or "affect."
In this sentence, 'влияют' is used to express the influence or effect that environmental issues have on something else, specifically people's health.
Экологические проблемы значительно влияют на здоровье людей.
Environmental issues significantly affect people's health.
Here, 'влияют' demonstrates how various factors (teaching methods) have an impact on the subject (students' comprehension).
Разные методы обучения влияют на уровень усвоения материала учениками.
Different teaching methods influence the level of material comprehension by students.
In this example, 'влияют' describes the causal dependency or impact that the weather conditions have on the outcome of agricultural production.