The phrase "common alleles" refers to versions of a gene that are frequently found in a population. It means that these variations of the gene are more commonly inherited by individuals within a group. Full definition
The density of C > G SNPs in this 10 % of the genome is also very high, with considerable variability in the frequency of the less common allele. (decode.com)
In contrast, more than 70 other common alleles have been associated with breast cancer susceptibility, most of which confer only a mild to moderate increase in risk. (ashg.org)