Operators and functions are routines that are built into the Perl language to do stuff.
The difference between operators and functions in Perl is a very tricky subject. There are a couple of ways to tell the difference:
Functions usually have all their parameters on the right hand side
Operators can act in much more subtle and complex ways than functions
Look in the documentation - if it's in perldoc perlop, it's an operator; if it's in perldoc perlfunc, it's a function. Otherwise, it's probably a subroutine.
The easiest way to explain operators is to just dive on in, so here we go: