Want some advice?
Forget about 'whilst'. You will never need it. If you see or hear it, just replace it with 'while' in your mind - it has exactly the same meaning. You will never need to actually use the word 'whilst'.
As Greg says, the word 'while' has many uses: a noun ( 'I spent a while there'), a verb ( 'You can while away the hours') and a conjunction ( Will you wait for me while go to the bank?).
'Whilst' is an alternative to 'while' only when it's a conjunction. It's also much, much rarer than 'while'. Most speakers of American English never use 'whilst' : to Americans i.e. the majority of English speakers in the world - it sounds outdated and pretentious. It is used sometimes by some British English speakers, but not by everyone.
A personal note: I'm British, I'm older than most members here, and the English I speak is more traditional, and possibly more 'formal', than many people's. And guess what? I never use 'whilst'. So if I don't need it, you certainly don't!