Alleles are alternative forms of a gene that arise by mutation and are found at the same place (locus) on homologous chromosomes. They control the same trait but may result in different expressions of that trait.
Let's analyze the options:
(a) "...different position on non-homologous chromosomes...": Incorrect. Alleles are at the same locus on homologous chromosomes.
(b) "...same position (locus) on homologous chromosomes and that cover the same trait": Correct. This accurately describes alleles. For example, the gene for flower color in peas might have an allele for purple flowers and an allele for white flowers, both located at the flower color locus on homologous chromosomes.
(c) "...same position on non-homologous chromosomes...different trait": Incorrect on both counts regarding chromosome type and trait.
(d) "...same position on homologous chromosomes...different trait": Incorrect. Alleles for a specific gene control the same trait (e.g., flower color), though they may lead to different phenotypes (e.g., purple vs. white).
Therefore, option (b) is the correct definition of alleles.
\[ \boxed{\text{two genes that occupy the same position on homologous chromosomes and that cover the same trait}} \]