This command is configured on links on which you dont want to be sending out periodic broadcasts like RIP (ver 1) would normally do. Eg: WAN links which needs to utilised as per demand (charged per usage).
Triggered updates allow rip to send updates over a link when there has been an update in RIP database, suppressing the normal periodic updates.
So if you have RIP running over a link for which you are charged for usage, you might want to configure triggered extensions. And, yes it should be configured on both ends, otherwise the router at the other end for which triggered extensions is not configured will keep sending out periodic updates.
http://www.cisco.com/en/US/docs/ios/iproute/configuration/guide/irp_cfg_info_prot_ps6441_TSD_Products_Configuration_Guide_Chapter.html
HTH
Lejoe