I had never come across that term before either, but Uncle Google pointed me to a Pentaho definition of it :
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.
Various software vendors have different swerves on the definition, but all seem to imply that their software is very good at it
You can achieve that by giving specific data level security & report level security for the user.
Also, If you want to send those report via email, you should opt for Qlik Npriniting product.
You can not send Report in Stanalone Qlik Sense. However, It can be achieved via Extensions.
But i would recommend to use Npriniting.
There is a different module called NPrinting, which can help you to send the reports to multiple recipients in various formats like Excel, PDF etc.
More help can be found in below link.