The job requirement basically wants the prospect to have experience with a project that you were in charge in which you might or might not have people following your lead. If you have that sort of experience and you are planning to mention it, make sure you succeeded on it.
If you don't have a PM experience, then the best things to do is to be pro-active and look for a project at your current job. If for some reason, you can't get a project under your belt, then start an open source project and try to get people on board. Even if you are a solo developer, you will learn a lot things about software project management.
I started my open source project and I'm learning project managament (PM) techniques. I'm even learning and rating myself as working developer because I'm both, my manager and developer, so my manager side set task and estimation and my developer side commit to those tasks. Now at work, we are starting a project and now I feel more confident know to commit for a particular requirement and how to estimate their delivery.
On techniques for open source sofware PM:
Discovering features....sometimes not even the customer knows what (s)he really wants.
Translating features into requirements.
Estimating requirements.
Prioritize the requirements and pick the ones that fit in a iteration.(What are the most basic requirements that can fit in one iteration?)]
Set milestone and iterations.
Break up the problem. (domain analysis)
Early design (just-good-enough design).
development (test, implementation, etc)
At the end of the iteration analyze your performance and feed-backs. Did I deliver what I promise? What went wrong? What I did right?
Also Learn how to scope with CHANGE. Seriously, At the middle of your iteration, you or your customer will find out that there is very important feature that if you don't it, the project is dead. Most likely, your only constant in your project is change!