Information adapted from Fiske Countdown to College.
In a word, nothing. You can major in economics and then go to law school, or you can major in ethnomusicology and then go to law school. It makes no difference as long as you have good grades, do well on the LSAT, and submit a great application.
Premed is the same way. Though you do need to take a selection of biology and chemistry courses, as well as calculus, premed is an advising program, not a major.
The same cannot be said about engineering or architecture majors, which are so packed with required courses that they leave little room for electives.
Majors in business are somewhere in between: they have plenty of requirements, but offer more flexibility than those in engineering or architecture to take outside courses or pursue a double major.
If you have even a fuzzy idea of a possible major, check it out on a college website and see what is required.
Every college works a little differently, so check with colleges you're interested in to see how majors and advising programs work.