Aniston is known for being a very private person and not doing many television appearances. She only seems to do them if she is promoting a new film or project. For this interview she was promoting Cake where she is the main character in a film about a women whose life falls apart. The interviewer asks what events in her real life helped her get into character for this role and how she prepared for the dramatic scenes.
This was an interview for CBS which is primarily a news channel. Because of this, most of the audience is adults. CBS doesn't have a lot of shows for teens or children, but they have comedy shows in the evenings for adults and talk shows in the mornings that are catered to an adult audience. Sunday morning shows on television tend to be very calming and relaxing and not dramatic in any sense of the word. This interview fits that theme because it comes across as very casual and seamless.
The purpose of this interview is definitely for Aniston to address her new movie and how it is so different from all of her other roles. They also address her divorce from Brad Pitt and how she and her now fiance keep their private lives private. Her primary purpose for doing this interview was to promote her movie, but she also opened up a little more about her life than she usually does.
The interviewer is very important in any interview because he or she shapes your perception of the interviewee. The follow-up questions they ask and the comments they make influence your impression of the person that is being interviewed. In this case the interviewer asked some personal questions when it came to her divorce and her childhood. He obviously wanted to learn her life story and how she became the person she is today. In this interview she is portrayed as a hardworking actor who loves her job but dislikes some of the consequences of being in the Hollywood industry.
Jennifer Aniston doesn't do much press, but when she does she tends to open up about her life while keeping the interview light and relaxed. This was a relatively serious interview catered to an adult audience, while still having moments of comedic relief.