How do researchers affect the funding opportunities of their department
A few quick points:


Many grants have evaluation criteria that incorporate the research environment of the investigators. Thus, the research ranking and status of researchers in the department and the university of the investigator can influence the chance of getting a grant.
Researchers within a department can help each other do good research in a wide range of ways. Senior researchers often mentor and teach more junior researchers. Researchers often collaborate within a department. This is both easy, because you are collocated. It also often aligns well. I.e., an academic is not only helping his own research track record, but he or she is helping the research output and capacity of the department. 
If you do good research and increase the prestige of the school, this can have a range of other beneficial effects for the department and other researchers. Academic visitors may be more keen to visit. Good PhD students may be more attracted to the department. And so on.


So in general, the contribution of a single academic to a department's research status is often only modest, but it is still meaningful. And in extreme cases, where the department recruits a research superstar, the effects can be profound.