I would say flexibility (TMTOWTDI) is a blessing and a curse: it made it incredibly easy for me (a biologist, mind you) to quickly learn how to write really bad (but functional) code.

Most of what I, personally, use perl for is bioinformatics which involves a lot of text parsing and many regexes. So, for me, the most-indispensable part of the language is the wonderful regex support. If I wanted to make this point to others I might show some sample code for extracting some data from a flat-file using perl (~1-3 lines) versus C, Java, or the like (many many lines). To me that would be most-compelling and is Perl's primary strength.

Update: Oh yeah! also CGI (CGI.pm). I don't know if it's relevant to your needs or not, but Perl is awesome for building custom web apps. A side-by-side comparison of a simple CGI script written in perl versus C would speak volumes, IMHO.