How does throwing and catching exceptions differ from using setjmp and longjmp?

The throw operation calls the destructors for automatic objects instantiated since entry to the try block.

Exceptions are in the mainstream of C++ now, so most programmers, if they are familiar with setjmp and longjmp, should know the difference. Both idioms return a program from the nested depths of multiple function calls to a defined position higher in the program. The program stack is "unwound" so that the state of the program with respect to function calls and pushed arguments is restored as if the calls had not been made. C++ exception handling adds to that behavior the orderly calls to the destructors of automatic objects that were instantiated as the program proceeded from within the try block toward where the throw expression is evaluated. 
It's okay to discuss the notational differences between the two idioms. Explain the syntax of try blocks, catch exception handlers, and throw expressions. Then specifically address what happens in a throw that does not happen in a longjmp. Your answer should reflect an understanding of the behavior described in the answer just given.
One valid reason for not knowing about exception handling is that your experience is exclusively with older C++ compilers that do not implement exception handling. I would prefer that you have at least heard of exception handling, though.
It is not unusual for C and C++ programmers to be unfamiliar with setjmp/ longjmp. Those constructs are not particularly intuitive. A C programmer who has written recursive descent parsing algorithms will certainly be familiar with setjmp/ longjmp. Others might not, and that's acceptable. In that case, you won't be able to discuss how setjmp/longjmp differs from C++ exception handling, but let the interview turn into a discussion of C++ exception handling in general. That conversation will reveal to the interviewer a lot about your overall understanding of C++.