This is a region-specific question–Indian English
I have noticed when working with colleagues from India that they use the word 'doubts' where the typical American would use the word 'questions' or 'concerns'. This is most prevalent at the end of a meeting or discussion where an Indian colleague will ask "Do you have any doubts?"
I have noticed the same word being used in the same way on several StackExchange forums (I assume from Indian users) and I'm curious how this word came to be used this way in India. I don't think I've ever heard this in British English (should that be the Queen's English?), so I doubt it started directly during the colonization period.
How, then, did it come about?
Edit-clarification for some very good point already provided in answers below:
In current American English, 'doubt' could be considered to be a synonym of 'question', but the difference is that 'doubt' implies lack of belief rather than lack of knowledge.
For instance, a math teacher may explain that any number raised to the 0 power is 1. For the uninitiated it may seem counter-intuitive because raising to a power implies multiplication and any number multiplied by 0 is 0, not 1. In this case an American student might say "I have doubts", meaning "I don't believe you", rather than "I don't understand you."
Best Answer
The use of doubts to mean questions is, AFAIK, Indian and also Spanish and Portuguese. See here for an explanation.
As I said elsewhere, saying "tengo una duda" (I've got a doubt) when putting your hand up is a common way to make a question in class for kids in Spain. It makes me wonder why English views interaction in terms of answering questions whereas Spanish (and Portuguese) sees it in terms of clarifying doubts. :-)