Hello Pradyumna
The show ip ospf database command shows the OSPF database found within the local router. This database consists of all of the LSAs that have been received as well as those generated by the local router itself.
The additional router keyword makes the command display information only about router LSAs, or Type 1 LSAs. By adding the 192.168.12.1 address at the end, you are specifying that you want to see LSAs originated by the router with that particular router ID.
So the command show ip ospf database router 192.168.12.1 displays Type 1 LSAs that have originated from the router with an ID of 192.168.12.1 or R1.
The purpose of the lesson was to show that by using distribute-lists the 1.1.1.1/32 network advertised by R1 is found in the OSPF database of R3, but is filtered from appearing in the routing table. By using the above command, Rene showed that this network still appears in the OSPF database as a received LSA, but not in the routing table.
I hope this has been helpful!
Laz