The conjunction whilst means the same as while. For Americans the word tends to have an archaic ring, so it is rare in American English and tends to give the impression that the writer is either British or affecting a British voice. There is less prejudice against whilst outside the U.S., however, and the word is fairly common in British publications (though all the British style books we checked recommend while over whilst).
With each of these examples, note that replacing whilst with while would not change the meaning of the sentence:
The broker says only 4% of stocks it covers have upside risk to consensus earnings estimates, whilst 9% have downside risk. [Wall Street Journal]
If you’ve ever found a fossil or a strange looking rock whilst on the North Yorkshire coast and wondered what it is, wonder no more. [BBC]
Whilst mining stock’s earnings are still expected to grow, this is from an extremely large base and at much smaller rates historically. [Sydney Morning Herald]
The provincial government spent over R1m on security whilst the clinic was standing empty after completion. [News24]