My response could serve as a prequel to the sufficient and useful ones you've received so far. It is more philosophical in nature.
This is a great question, although it seems trivial and boring at first. If I may draw the analogy to the movie Karate Kid. Mr Miagi asks the karate kid to clean his house with the "wax on and wax off" movements. Only after it became a habit and after he mastered the movements did the karate kid understand why he was doing it in the first place. Similarly, if you've (1) done sufficient research about consulting as a sector/career, the firms you are applying to, the skill sets you gain, the experiences and exposures you gain, and the people you meet; (2) defined your objectives by working in this field; (3) networked enough with current and ex-consultants, your answer to this question will come very naturally. If you are struggling with responding to this, it is a sign that there is still a knowledge gap against what you know about consulting, your career objectives and your knowledge of the firms and what it really is like.
To answer your other concerns:
1. How long & specific/vivid should an answer be?
Limit your response to under 3 minute. In interviews, you are expected to be able to deliver the message when asked and to do so directly. The response should be personalized although may overlap with general responses. Be specific on how you arrived to that "why". For instance, spoke to 50 people in the firm and loved XYZ about it.
2. Should it be answered in a structured manner as well; i.e. "There are X reasons why I choose consulting / MBB.... First is .... Second is .... "?
Don't over structure the response to these questions. They want to see your natural side as they will be assessing if they'd want to work with you as well. Be structured when solving problems and communicating complex ideas/thoughts. Otherwise be natural yet direct and to the point. There's no harm in being a bit structured.
3. Other things that need to be considered when answering these questions.
This question is more important to you than to the firm. Before assessing how they would view or take your response, it should truly be the right one for yourself. You need to know why, align your personal objectives, pick the right firm, be entirely convinced and happy with your choice and then respond.