Hi-C is a chromosome conformation capture technology whose aim is to give an idea on how chromosomes fold and associated with each other. For example, knowing the conformation of a chromosome allows you to understand the relation of genes and enhancers. Looking into the literature you will see a large array of applications. Hi-C has been instrumental in the characterisation of the so called Topologically associating domains (TADs) that are stable building blocks (apparently they are folding units) present in all eukaryotic studied so far.
I personally think that Hi-C together with many other conformation capture methods, are disruptive technologies that are quickly changing our understanding of genetics by allowing us to move from the 1D analysis to 3D interpretations.
First, I would recommend to go through "xC" (chromosomal conformation capture) technologies: http://www.ncbi.nlm.nih.gov/pubmed/19588093. Actually in early times people were doing FISH analysis and counting the number of cells that have two marked regions in close proximity to see if given chromosomal regions are in contact.
HiC basically gives you a map of contacts between all pairs of genomic loci. Todays resolution allows you to split the genome into 0.5-1Mb regions and to get an estimate of contact frequency between a pair of regions on the same/different chromosomes.
HiC is most useful in fundamental research and can help to link epigenetics with physical chromatin interactions and positioning in the nucleus. It can also be used to see how the DNA is folded during various cell cycle stages, etc. This approach could also be used to probe if spatial positioning matters when dealing with "fragile" (frequently mutated) DNA regions, therefore it is important in cancer research.