Will you require sponsorship to obtain, maintain, or extend your employment authorization?

If you are unsure about what this question means, then I think I can help you. 
What this person (I'm assuming a possible employer, or perhaps a person you talk to in order to obtain a Visa) means by this question is whether you are actually authorized to work in that particular country. So, for example, if you live in the US, but want to move to, let's say, Japan to work, you will probably get this question. It means that the employer may give you a sponsorship to help you get a working Visa for that country. If you don't require such sponsorship, it means that you already have such a Visa and can work in the country already.