Example of a problem with structured output labels
Structured Learning is basically learning prediction functions that is used to map input data to complex output space.
The regular SVMs are used for univariate classification where input is mapped to atomic labels or regression where input is mapped to vectors or scalar numbers.
Structured Output learning extends this very process to more complex output spaces like:
- Multi Class Classification : where output is a "set" of class labels.
- Object localization Problem : where output space defines bounding boxes. 
- Sequence alignment problems in protein homology detection,
- Parts of Speech tagging in NLP , etc. 

Hope this clears it up for you.