Hello,
I'm hoping this helps:
Reader Extensions is a module that you can purchase from Adobe and that can be installed as part of the LiveCycle framework. Once installed, you can access the service as part of your workflow. For example, you may produce a workflow that consists of 3 steps:
1. Access some data from a database
2. Merge the data with a template and produce a PDF
3. Reader extend that PDF
You would Reader extend (step 3) so that people who have the free Reader installed on their computer will be able to access functionality that normally would only be available to people who purchase Acrobat (i.e. digitally signing a form, saving data offline, etc)
Reader extensions works by digitally signing the document with a specific credential. That credential is recognized by Reader as enabling certain rights/features to that document.
Hope that helps