Dominance explains the relationship between alleles in determining the phenotype. Consider two alleles
A is dominant, then individuals
AA and individuals
Aa present the same dominant phenotype while individual
aa present the recessive phenotype.
Selection and dominance
When you ask
A recessive allele can become represented in a significant number of individuals in a population, how?
I am not sure why it seems unlikely to you. No one said that the recessive phenotype was less fit than the dominant genotype.
If the alleles
A are present at the same frequency in the population, then most individuals will carry the dominant phenotype. But the alleles
a may well not be at the same frequency. Selection (as well as other evolutionary processes that I won't talk about here) will affect the frequencies of these alleles. If the dominant phenotype has a higher fitness than the recessive phenotype, then the allele
A will increase in frequency. If, on the other hand, the recessive phenotype has higher fitness than the dominant phenotype, then the allele
a will increase in frequency.
From allele frequency to genotype frequency
Let $p$ and $q$ be equal to the frequencies of the allele
A, respectively, such that $p = 1-q$ is necessarily true. Under a few assumptions (see here), the frequencies of the genotypes
aa are $p^2$, $2pq$ and $q^2$, respectively. For more information on why this is true, you can have a look at Solving Hardy Weinberg problems.
Let's imagine a scenario where, the recessive phenotype has a higher fitness. The allele
a will increase in frequency in the population until eventually reaching a frequency of $p=0.95$. At such allele frequency, $0.95^2 = 0.902$ (or 90.2%) of the population will carry the recessive phenotype.
Note that at very low frequency of the recessive allele, the recessive phenotype is very rare (as it's frequency is the square of the frequency of the allele) and there is almost no selection acting on the locus of interest. But all of that is a story for another time.