I replied to this question on a Linked In forum so thought it was worth repeating here. If I was an employer, I would want to ask this question of any admin who was applying at my organization.
Since it is almost second nature to most admins to be organized it is sometimes difficult to answer, but it is just for this reason that it needs to be asked. An admin has to be a strong organizer so they don't want to hire someone who isn't.
When answering this question think about what you do when you first come in in the morning. After I turn my computer on and it is loading, I check my voicemail messages and write anything down that I need to follow up on, action or pass along. I then go through my emails and prioritize what is urgent for the day. Our job is to keep our boss organized, so at the end of the day I get everything ready for him for the next day by providing meeting materials, travel tickets, reservation information etc. I do this by having a good bring-forward system and then I explain my system of ensuring I have everything when I need it.
I make checklists so nothing is missed and I have a to-do list for daily work but also for projects to keep things on track. To keep my boss organized, I also need to be organized by keeping my desk clutter free and having a place for everything and within easy reach. I also pile my work to the left of my computer in order of priority. It often gets reprioritized as more urgent matters come up but it is a good system. I have what I call a Wait bin where I put things that I am waiting for an answer. I go through this each morning to see if there is any follow up I need to do. I also do this with my emails and have a TO-DO folder where I put anything I need to follow up on and go through that each day.
You should always try to give real examples in an interview. Think about a big project you've successfully completed and then walk them through how you accomplished it. They will then have confidence that you are able to to the job.
A big mistake some employers make is to assume that anyone can do our job. It is a smart employer who asks this question.