Example:- Flushing data page in a case via activity or DT- suppose you are using a thread level data page and you have fetched data of a customer using data page, D_Customer [AccountNo-123]. If we have a mechanism to update customer details, and assume this particular customer details has got updated in the backend but in your case clipboard you already have D_Customer [AccountNo-123]. So when you again hit this data page you will get data from this clipboard data page not the updated data. Before hitting this data page for the next time you can flush this dpage by pzFlushAllinstancesofdatapage() function so you will get the latest data because that dpage will be created freshly.
To conclude- we flush data page to remove instances of that particular dpage from the clipboard so that when we fetch data using that dpage, we will be getting updated data. If instances existed in the clipboard, data will be fetched from that dpage(old data).