In it's simplest form the idea 'progressive data capture' is that you only ask the user for the data you need when you need it.
The problem it solves is form abandonment - the more you ask your users is a single go, the more they are likely to give up and go away.
I have done some work on an offers site and used this method to capture data from the users: To sign into the site and maintain an individual users profiles they simply need a username and password - I used an email address for user name to add the ability to validate the user. At this point I can start collecting behavioural information (what sort of items they click on, what searches they perform, etc) associated with each particular user to help taylor their experience a little more. If they select an offer that only requires an email address then they don't need to add any further information but, if they select an offer that requires a postal address, then they are prompted to add one. They can, of course, do this at any time by editing their 'profile' but the important thing is that they are not asked for it until it is needed. In other words, don't ask your user for all the information required to perform the most complex task on your site unless they are actually going to perform that task.
As this is really subjective to the application I'm not sure that you'll find any solid research or best practice info. A search for 'form abandonment' on Google yeilds a lot of results all talking broadly about the same thing though.