"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.
The obvious difference between science and Big Industry is the benefits of a united front. Businesses stand to benefit by cooperating to push a dishonest viewpoint that flatters the industry Scientists, by contrast, gain face by disproving each other's theories, and the more widely touted a given theory is, the greater the prestige of defeating it.
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.
- An astronomer can enjoy a long and meaningful career continually proving Einstein correct. But prove him wrong, and future astronomers will enjoy long and meaningful careers proving you correct.