Talking points are useful for a person or organization as shorthand and as an outline.
Say there's an 8.7 magnitude earthquake in Indonesia and every is wondering if a tsunami will swamp Hawaii before turning Los Angeles and the rest of the West Coast into wetlands.
The government will naturally turn to scientists who've dedicated their lives to studying earthquakes and tsunamis. But sending those guys in white lab coats loose on CNN without any preparation might is a bad idea.
Television, radio and newspapers work in soundbites. Professors and scientists are used to giving hour-long lectures and seminars.
Talking points are useful in situations like this.
The public relations folks at the federal government would talk to their experts on tsunamis and get all the right information. Then they'd distill it into a page of talking points, summing it up for the press and public in a way they can understand -- and send those talking points to state and local authorities on the West Coast, so they can answer questions from their local press and citizens.
If used at a press conference, talking points aren't a script. They're used as a guide and reminder.
Talking points can be persuasive or informative, so you can use them as the framework to create other products and events -- a press conference or a guest column, a newsletter or a web site.