The authors do a Genome-Wide Association Study (GWAS) analysis, which is a study of whether any particular loci in the genome are associated with a particular phenotype (in this case, skin pigmentation levels).
GWAS analyses look at variants (alleles) across the whole genome, rather than focusing only on regions that are thought to be associated with a phenotype. This way, new regions of the genome can be discovered as being involved in the genetic architecture of a trait.
The authors control for age, sex, and genetic relatedness, because these are variables that could confound (confuse) the results by affecting the phenotype of interest, in this case skin pigmentation. To avoid confusion, the authors take these variables into account when they look for associations between SNPs and skin pigmentation.