Robert's Perl Tutorial
Subroutines are oft-used pieces of code. They exist so you can re-use the code and not have to constantly rewrite it.
A module is, in principle, similar to a subroutine. It is also an oft-used piece of code. The difference is that modules don't live in your program, they are their own separate script outside your code. For example, you might write a routine to send email. You could then use this code in ten, a hundred, a thousand different programs just by referencing the original program.
As you would expect, the basic Perl package includes a large number of modules. These have been written by people who had a need for the code, made it a module and released it into the big wide world. Many of these modules have been debugged, improved and documented by yet more people. To quote the OpenSource mantra, all bugs are shallow under the scrutiny of every programmer.
Aside from the many modules included with Perl there are hundreds more available on CPAN, the Comprehensive Perl Archive Network. Refer to your documentation for details.