A classical example of a Block in a report would be the following:
Suppose you had a secondary loop through Devices for a report on Ranges. For each Range, you want to print a header, the Devices relating to that Range, and then the Range footer. Naturally, if there are no Devices relating to a Range, because they for example have been filtered out, you wouldn't want that entire Range to print. To achieve this, you would make the Range header the Block Start and Suppress it, and the invoice footer the Block End and Suppress that too. The actual band with the Device info on it, however, should be left alone.
The effect that this will have is the following: If there is at least one record in the secondary loop that does not get filtered out and its associating detail prints, all the details within the block will print. However, if there are no valid records and hence no details for Devices print, none of the other details (i.e. the Ranges header and footer) will print either.
In your Report Structure List, the stars represents bands with "Suppress if Block Empty" switched on, the closing angular bracket indicates a block start, and the opening angular bracket indicates a block end.