Unless the interviewer has a really dry sense of humor, they probably won't appreciate this response as they are taking time out of their day to ask you questions to see if you are a good fit for this role. As Business Analyst, your job (and this is my personal opinion about the role) is to take non-technical requirements from users who don't understand the nuances of software development and feature implementation, and turn them into technical specs that can then be implemented by the developers into a product the company can then sell back to the client or other prospective consumers.
To be a bit more clear, let's take a look at what I think is a great software developer question and how it should be answered. "Why are manhole covers circular?" I've discussed this question with a guy who does interviews almost daily and he says he asks that question for two reasons. 1) Given a seemingly trivial or odd question, can you come up with something of substance? 2) What's your problem solving process?
He mentioned that good candidates started immediately throwing out ideas, no matter how silly they may be, and the best candidates would start to think technically about the problem, things like structural integrity of a circle vs a square, cost of material to produce, etc..
If we apply this logic to the statement you were given, I would imagine they wanted you to take an idea and start rolling with it to see where you go. Maybe you have an idea for a silly invention or website you've been thinking of creating. I would say it would benefit you greatly to sketch a quick design of that product and start working through the logistics of making it, marketing it, thinking of pitfalls, listing requirements, things like that.
All of this being said, I think asking someone right from the start "Write something on the board" is a bit silly to ask (personal opinion on this, might be a common question in Business Analyst roles). You'll find there are some interviews where the interviewer simply doesn't do a good job or the company is not a good company to work for and you dodge a bullet by being asked questions like that. In the future, if you are asked a question like that, just ask for some clarification or start writing stuff on the board that a Business Analyst might record and you should be in the clear.