The technique I mean is where the profile page will say "You have completed 60% of your profile, fill in your x, y and z to get to 100%". I think this is a very powerful technique but I can't remember what it's called so I can't direct my boss to any articles about it. I think it ends in 'bar'.
The ui control or pattern for this is Completeness Meter (See the ui pattern for this). It's sometimes called a Progress Bar, but that term also has a much more generic use - such as in the case of a download percentage, and less specific to the sort of profile completeness you are talking about.
The underlying concept is that of Gradual Engagement. The profile completion percentage is a motivator to increase the amount of information given to the website, but essentially it's all about gradual engagement. Other terms include progressive disclosure but I prefer gradual engagement - especially since the term has stuck thanks to the likes of Luke Wroblewski - see his pages on this topic - and his preso on why sign up forms must die
This is a form of gamification, too. As users will want to reach 100% completion, like in a game, they will strive to complete their set tasks. Especially if there is some form of reward at the end of the 100%. http://www.dropbox.com do this especially well where they reward their users with extra storage if they complete set tasks and get to 100% completion.
The only reason I'm on stack exchange is to receive badges!! So give this one a vote ;) I'm a newbie you see.
Jakob Neilsen describes this best:
On the Web, usability is a necessary condition for survival. If a website is difficult to use, people leave. If the homepage fails to clearly state what a company offers and what users can do on the site, people leave. If users get lost on a website, they leave. If a website’s information is hard to read or doesn’t answer users’ key questions, they leave. Note a pattern here? There’s no such thing as a user reading a website manual or otherwise spending much time trying to figure out an interface. There are plenty of other websites available; leaving is the first line of defense when users encounter a difficulty.
You are probably referring to "Endowed Progress Effect"