A “big man on (the) campus” (BMOC) is a male student who is highly popular. He could be a star athlete, a star student, a wealthy celebrity, a class president or popular in other ways. The term is somewhat dated and there doesn’t seem to be a popular “big woman on (the) campus” (BWOC) term.
 
“Big man on the campus” was printed in The Daily Northwestern (Northwestern University, Evanston, IL) and the Los Angeles (CA) Daily Times in October and December 1911.
 
“It is hinted one of the men placed on probation for the coming year is one of the B. M. O. C. (in student slang, meaning Big Man on the Campus.)”—at the University of Michigan—was printed in the Detroit (MI) Free Press on May 26, 1923.
   
         
Wiktionary: big man on campus
Noun
big man on campus (plural big men on campus)
1. A highly popular male collegian.
 
(Oxford English Dictionary)
big man, n.
North American. big man on (the) campus (also with capital initials): a (superlatively) popular or influential male student at a college or university. Abbreviated BMOC.
1923   Life 11 Jan. 22/2   Mr. Benchley is..the President of the Senior Class, the Captain of the Crew,..and the one Big Man on the Campus.
1943   Chicago Tribune 25 May 10/6   Today’s big man on the campus doesn’t sit spooning on sorority steps in the moonlight.
     
16 September 1896, The Examiner (San Francisco, CA), “Stanford Greets Cross,” pg. 10, col. 3:
Captain Fickert has been disposed from his position of the most conspicuously “big man” on the campus, for Cross is taller by an inch, and his six feet three is matched by magnificent breadth of shoulder and depth of chest.
       
19 October 1911, The Daily Northwestern (Northwestern University, Evanston, IL), “Bunch Leads Y. M. C. A.,”
It is not the honor a man has won that makes him a big man on the campus.
   
28 December 1911, Los Angeles (CA) Daily Times, “New Year’s Game Planned” by Owen R. Bird, pt. 3, pg. 2, col. 2:
This showed a wonderful college spirit and Cass was made a big man on the campus.
 
22 May 1920, The Tar Heel (University of North Carolina, Chapel Hill, NC), “Mikado to be given Friday night at 8:30,” pg. 2, col. 4:
“A big man on campus he’s stood,—so,
Would I be the man of the hour?”
 
11 January 1923, Life magazine (New York, NY), “The Latest Books,” pg. 22, col. 2:
Perhaps too young to be the Dean of American Humorists, Mr. (Robert C. - -ed.) Benchley is easily the President of the Senior Class, the Captain of the Crew, the holder of the McWhimsey Scholarship and the one Big Man on the Campus.
   
7 April 1923, Worcester Democrat (Pocomoke City, MD), “Frank Views Of A Teacher” by A College Instructor, pg. 4, col. 4:
“He has not become a ‘big man on the campus.’ Such pre-eminences requires a rather large amount of misapplied force.”
   
26 May 1923, Detroit (MI) Free Press, pg. 13, col. 5:
BOOZE PENALTY SPLITS CAMPUS
Secrecy of U. on M. Discipline for Drinkers Scored; Daily Hits Rum Trade.
Ann Arbor. Mich. May 25.
(...)
It is hinted one of the men placed on probation for the coming year is one of the B. M. O. C. (in student slang, meaning Big Man on the Campus.)
 
16 May 1924, The Daily Northwestern (Evanston, IL), “Do Activities Pay?,” pg. 2, col. 1:
Students have no reason to fear the future, the “big man on the campus” the least of all; he is well prepared.
 
19 June 1932, Hartford (CT) Daily Courant, pg. 10, col. 4:
Big Man On Campus’ Not ‘Bookworm’
Earns High Salary After Graduation
 
30 October 1934, The Daily Northwestern (Evanston, IL), “Collegiate Opinion,” pg. 4, cols. 3-4:
The neophyte sees every active member of the fraternity as a BMOC and if the active members conduct themselves in the right manner the results will be seen in a real pledge class.
 
13 November 1934, The Daily Northwestern (Evanston, IL), pg. 1, cols. 2-3:
Are You BMOC? Don’t Be a Snark—Wangle
(...)
BMOC—big man on campus.
 
19 June 1935, Ames (IA) Daily Tribune-Times, “College Grads Go Job Hunting But Leave Diplomas in Bureau” (U.P.), pg. 1, col. 6:
He’s proud of having been a B-M-O-C (big man on the campus) but doesn’t boast about it.
   
23 October 1937, Decatur (AL) Daily, “Alabama Proves Good Training Ground For Statesmanship Records Reveal,” pg. 2, col. 1:
To three of the remaining eight, the collegiate term “BMOC” (Big Man on the Campus) may very definitely be applied.
 
8 November 1937, Albany (OR) Democrat-Herald, second sec., pg. 1, col. 5:
STUDENT SLANG IS ‘IN THE SWISH’ SAY YE OLD GRADS
Albuquerque, N.M.
(...)
Slang current on the modern campus includes:
B.M.O.C.—Big man on the campus.
 
Wikipedia: Big Man on Campus
Big Man on Campus (also known as The Hunchback of UCLA and The Hunchback Hairball of L.A. in the United Kingdom) is a 1989 comedy film directed by Jeremy Kagan, and written by and starring Allan Katz. It is loosely based on The Hunchback of Notre Dame by Victor Hugo. The film co-stars Corey Parker.
     
Top Universities
The Lazy Man’s Guide to becoming the Big Man on Campus
Written by Thomas Ahonen
01:00AM Jul 19, 2012
This week, I’m using my psychology degree to give you tips on how to experiment with your life to make people think you’re the big man on campus (or big woman on campus) that everyone should get to know… with little to no effort at all!
 
Urban Dictionary
big man on campus
A guy in college with connections. The Big Man on Campus (or BMOC) knows people. He’s privy to the locations of the best parties, the coolest hangout spots, and the loosest women. The term isn’t used as much anymore due to the advent of internet social networking, allowing everyone to “know people”; but still, being a BMOC takes skill in real-world networking. BMOC’s aren’t always douchebags, but may have a slightly more inflated ego than most.
(...)
by AR-558 March 16, 2013
   
Google Books
The New Partridge Dictionary of Slang and Unconventional English
Edited by Tom Dalzell and Terry Victor
New York, NY: Routledge
2013
Pg. 234:
BMOC noun
a popular and visible college boy US, 1934