"Big science" is a pejorative term used by creationists which they apply to any specific subjects or theories within science that do not fit with their viewpoint. The term is based on previous uses such as "Big Tobacco" or "Big Petroleum" which are generic terms for large companies that run the cigarette and oil businesses respectively. This is done in an attempt to characterise current consensus within the scientific community as being oppressive towards the 'small science' made up of opposing creationist view points.
Among the sane, "big science" refers to large, collaborative scientific projects that usually involve large, expensive items of equipment such as particle accelerators or satellites. This is contrasted with "small science" done by individual laboratories or smaller collaborations.
- Done by local Mom and Pop laboratories, which had been part of your community, passed down from parents to children for over 150 years before being forced out when that big-box chain synchrotron moved in just outside the town limits. Sure, their proton-proton collisions are a little cheaper (mostly because their protons are imported from who-knows-where in China), but do they know your name? Or remember your children's birthdays? I didn't think so.