Translation:Do you understand what the teacher is saying?
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Also, note that 什么 when used as a question word and 吗 ask two distinct questions. 什么 asks "what?" It is an open-ended question. The person answering needs to supply addition information, to answer the question. It is like answering a "fill in the blank" or essay question on a test. 吗 turns what would otherwise be a statement into a yes/no question. The answer is a "yes" or a "no". It is like answering a "true or false" question on a test.
So if you see 什么 and 吗 in the same sentence, 什么 can't be a question word.
In this context, both 明白 and 懂 have the same meaning of "understanding". When YOU apply the words in your own speech, the difference is that 懂 can be further applied to describe what you know (knowledge) or what skills you have. E.g. you can say 我懂英語 which means "I know English" (whereas when you say 我明白英語 it means "I understand how English works", which is a bit awkward we seldom say things like that), or for skills e.g. 我懂得使用Photoshop, "I know how to use Photoshop", whereas you cannot say 我明白使用Photoshop
I think the difference is expressed in English when we say "I don't get what he is saying" vs "I don't understand what he is saying", In the first expression we are saying that we don't understand the import or purpose of his words, we don't understand what his point is, we don't understand the gist of his meaning. But the second expression can just mean we don't understand the words, because we don't know the language he is speaking.