FROM PEOPLEBOOKS:
It is typically used when you are repeating the generation of a templated report layout many times for multiple like sets of data. For example, generating a batch run on vendor purchase orders or customer invoices. With bursting, you can generate individual report files resulting in separate secured output.

Real life example:
For ACH payments, we setup bursting on the Vendor. So each vendor only gets an email of "their" output/Remittance Notification for the automated payments.

So when you setup your XML Publisher's "Report Definition", the 'Bursting' tab was setup with Burst By: PARTY_ID
(as within ACH the vendor becomes referred to party_id).