Report Bursting has a fairly long history (for the computer industry). It can be traced back to the days when printers were the size of washing machines and printer paper was perforated fan-fold with green bars on it. Large reports would be created with 'page breaks' between each section of the report and someone would have to stand and physically break, or 'burst', the pages at that point by flicking the edge of the perforations with their finger.
Bursting is still used today but generally involves much less finger-flicking. Some reporting bursting solutions still use the approach of taking one long data set and breaking it up into many parts, however Pentaho uses an approach that is more sophisticated.