Amazon focuses the majority of its interview around behavioral questions paired to its Leadership Principles (LPs). These questions will assess (1) how you come up with ideas, (2) how you work with others, (3) how you execute, and (4) whether you can deliver results. Between the phone screen and the ~5 other interviews, they will typically assess you can across 12 LPs and along the way determine if you exhibit each of these LPs and have the necessarily product thinking, technical skills, and communication skills required to be a product leader at Amazon.
Communication at Amazon is extremely important so being able to answer their questions in a structured, concise, and clear way is essential to doing well in this interview. Also, you should remember that this is also an exercise in story telling. Your answers should follow a specific style and structure, but they should also be easy to remember, easy to follow, and at least somewhat engaging. Think of your answers as short stories.
Although every company has slightly different behavioral interview questions, if you prepare well for the Amazon style questions, you will likely be very well prepared for your other behavioral interviews.
There are several different frameworks that you can use to effectively communicate (e.g., Situation, Task, Action, Result; Situation Behavior Impact) but one that tends to work well is the following (Nugget + STOARL):
Most interviewers will use something similar to the below to determine if you have a good answer or not. Although not every story will allow you to hit all 6 points below, you should try to have as many of your stories as possible hit all 6.
Other new LPs: Strive to be Earth's Best Employer, Success and Scale Bring Broad Responsibility
TK