Nuclease protection assays are used to map introns and 5 and 3 ends of transcribed gene regions. Quantitative results can be obtained regarding the amount of the target RNA present in the original cellular extract - if the target is a messenger RNA, this can indicate the level of transcription of the gene in the cell. 
They are also used to detect the presence of double stranded RNA, presence of which could mean RNA interference. 
Northern blotting is a laboratory technique that produces similar information. It is slower and less quantitative, but also produces accurate information about the size of the target RNA. Nuclease protection assay products are limited to the size of the initial probes due to the destruction of the non-hybridized RNA during the nuclease digestion step.