1
general::
An urgent or crucial issue under heated discussion. For example, Real estate taxes are always a burning question for the town leaders. This term has exact equivalents in French (question brûlante) and German (brennende Frage). [Mid-1800s]
American Heritage Idioms
2
general::
Phrase(s): a burning question [and] the burning question
Fig. a question whose answer is of great interest to everyone; a question that needs very much to be answered, as a fire needs to be extinguished. • There’s a burning question that needs to be answered: Why did you leave your wife of only one month?
McGrawhill's American Idioms And Phrasal Verbs