The Restart Framework exists to cater for a deficiency within SSIS, that being the poor support for restartability. Let's define what I mean by restatability:
A SSIS execution that fails should, when re-executed, have the ability to start from the previous point of failure.
SSIS provides a feature called checkpoint files that are intended to help in this scenario but I am of the opinion that checkpoint files are an inadequate solution to the problem, I explain why in my blog post
Why I don't use SSIS checkpoint files
The Restart Framework was designed to overcome the shortcomings of checkpoint files. Note that the Restart Framework only supports SSIS 2012 at the time of writing.
Let's define some important terms that you will need to become familiar with if you are going to use the Restart Framework.
An ETLJob is the definition of some work that an end-to-end ETL process needs to perform. An ETLJob would typically incorporate many SSIS packages