MPI: cores or processors?

Hi I am kind of MPI noob so please bear with me on this one. :)

Say I have an MPI program called foo.c and I run the executable with

mpirun -np 3 ./foo

Now this means the program will be run in parallel using 3 processors (1 process per processor). But since most processors today have more than one core, (take 2 cores per processor say) does this mean the program will be run on 3 cores or 3 processors?

Probably this has to do with my poor understanding of what the difference between a core and a processor really is so if you could also explain a little more that would be helpful.

Thank you.