Universities and research centers frequently use grants and donations, both public and private, to augment existing research programs and to start new ones. The funding gets used to pay for operating expenses, research, travel, data collection, student stipends and staff support. Frequently, programs are lauded internally with more clout as their ability to generate outside funding increases.
Problems with corporate funding occur in two areas: a corporation being donor raises the question of whether the research is biased in the company's favor, and the objectivity of staff and faculty becomes questionable as they benefit from the private funding.
Universities frequently respond that receiving corporate donations generally doesn't violate any laws. Second, many schools point out that they have separate boards that dole out the funds rather than allowing direct relationships between faculty and sponsors. Third, the funding generates research that benefits society as a whole, so the ends justify the means.