In an excellent paper Frances Coppola (@Frances_Coppola) shows that disentangling structural fiscal balance from the budget balance is not an easy task as it relied on not easy to define hypothesis.
Therefore, the question on the importance of the concept is on the table. Can it be useful if its definition can be perceived as fuzzy? May be is it just a way for economists to speak a very specific language that will not be understood by non economist?

Her conclusion
“The aftermath of a severe negative shock is no time to be worrying about “structural” deficits. Better to restore the economy first, by every means available. Dealing with what would be better named the “residual” fiscal deficit is a job for the good times.”

Her article is here http://www.pieria.co.uk/articles/the_myth_of_the_structural_deficit