Haplotype: A specific combination of SNPs all occuring together on the same chromosome (i.e. all occuring on the chromosome inherited from Dad, or, inherited from Mom). Common DNA microarrays such as 23andMe, FTDNA and AncestryDNA's will at most identify the number of different alleles at each SNP location - 0, 1 or 2 - but can't identify which sides of the pair of chromosomes they came from. If matching SNP's are available for both parents, it's possible to determine which side they came from with high precision based on Mendelian inheritance, called phasing.
Because haplotypes are highly likely to be preserved in populations, there are several algorithms for attempting to conduct pseudo-phasing on large number of unrelated people. Sequencing, on the other hand, directly reads the sequence of nucleotides on a single strand of DNA, therefore preserving phasing. Next Gen Sequencing can thus provide not only perfectly phased genome, but also a haplotype map which can be used to impute untested SNP's from nearby known ones.
Haplotypes are important for example because many of the SNP's found by genome-wide association studies aren't the true cause but simply occur on same haplotype and are thus inherited together. This can lead to over-estimation of the risk by including odds ratio of different SNP's along same haplotype, or flip-flop phenomenon where the effect of the SNP is opposite in different populations due to population-dependent variation in the haplotype. Haplotypes have also important applications in genetic genealogy and determining identity by descent.