A good interview is a conversation where both sides do their best to figure out if the opportunity is a fit. Asking questions is essential for figuring that out. Your purpose in asking questions is to get a complete picture of the company and role. The more you know, the more likely you are to make the right decision.
The questions you ask will vary depending upon what role you are interviewing for and who you are talking to. A salesperson will want to know different things than an engineer. And you will vary the questions you ask to the founding CEO vs. a recruiter who just joined the company last week.
How big is the market for the product? How fast is it growing? Is this a stable market or one that is so cutting edge that nobody yet recognizes it's even a market? Is the market focused on consumers or businesses? Does the company have plans to enter new markets? If so, what are they and what is the timescale? Ask which market will you be working in, and what are the biggest opportunities and challenges?
How developed is the product? Depending upon the stage of the start-up you may be interviewing at a firm that only has an idea, or one that has a product that is already well adopted and generating revenues. Is the product going to change? What are it's biggest challenges? Is the company working on many different products or focusing on just one? How will product evolution effect your job?