how can a recessive allele become represented in a significant number of individuals in a population
A recessive allele is one whose phenotype can be masked by a dominant allele. A recessive allele is not necessarily deleterious, and the dominant allele does not necessarily have higher fitness than the recessive allele. Fitness and dominance are often confused, but they are not the same thing. 

In some scenarios, the recessive allele indeed confers a fitness benefit, and when it does, it is predicted to increase in frequency rapidly because homozygous recessive individuals have higher fitness than both homozygous dominant genotypes and heterozygotes.

A recessive allele can also persist in a population if it is deleterious in homozygotes but confers a heterozygote advantage. The most famous example of this phenomenon is in Africa, where individuals heterozygous at the sickle cell locus have a fitness advantage because they are resistant to malaria. A higher prevalence of sickle cell phenotypes occur because selection for heterozygotes maintains a high frequency of recessive alleles in the population. For more, see Templeton (1982, http://www.indiana.edu/~curtweb/L567/readings/Templeton.pdf) and Allison (1954, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2093356/).