This is purely US-centric: other countries have different funding models. This is also from the perspective of an academic with a Ph.D, rather than a graduate student
As Jamie and Peter point out, the primary purpose of funding is to support graduate students. A secondary purpose is to support yourself during the summer. It's not widely known, but most US-based academics aren't paid for the 3 months of summer, and use grant money as salary for those months (I'll not discuss the limitations of NSF vs DARPA etc etc).
So you say, "I don't need students, I'll just work with colleagues". Great ! but then you need money to visit them. Without grant money, you have to wait your turn for whatever meager departmental funds might be available for travel (usually minimal).
So you then say "Fine ! I'll use skype and email to collaborate". Great ! but then you need to travel to a conference to give a talk. How do you fund that ?
So you say "Fine ! I'll just publish in journals and on the arxiv, and the brilliance of my research will shine through". Um, yeah....
If you're a junior academic, not getting funding can also affect your ability to retain your job itself. Funding is a major income source for most American universities.
None of this is ideal. But that's how the system is currently structured, dating back to Vannevar Bush, the founding of the NSF, and the mutation of the university into a research-generating enterprise.