It is the most widely used programming language on earth, thanks to the popularity and accessibility of the Web. Programmers don't have all the time in the world, they need something that do powerful things and resembles English (or any practical language we humans like) so that it's easy to learn. They pick Perl often because of this.
An astonishing number of web users use it everyday and never know it. It's like that widget that keeps your fridge cold. Some widgets just don't advertise themselves.
Perhaps we don't want to hear about it, I can live with fewer logos and brand names personally--please hide the widget that makes the fridge code and don't tag it with logos.
Perl is different, you won't want it hidden, it's too useful. Like English. You want it exposed. Often used.
You need to use your brain, and feel fun and creative, have an itch to solve problem, possess copious amount of laziness so that you'll want to solve it with the minimum amount of fuss. But that's it.
Something simple and fun: I often find that my favorite online services are created using Perl. I learned to do this with a service call the Netcraft Website Finder (at www.netcraft.com). Consider writing down the web address to 10 of your most favorite websites and do a simple search on Netcraft. For example, my first entry is "www.everything2.com". After clicking on the go button I get an answer telling me that Perl is powering www.everything2.com! It's not always so straight-forward. If it says it's running Apache, Linux, mod_perl, or cgi or just some long winded phrase or product with any of those previously mentioned words--chances are that perl is an integral part of that web service. You may learn that few people will have a list where none of the sites use Perl.
Interesting things you can do with Perl: