Explain the relationship between dominant allele and inheritance of the trait it codes for

The dominant allele is the allele, which if present in the heterozygous condition, masks the effect of the recessive allele, either completely or partially.

In the normal conditions (exception being incomplete dominance), the progeny having dominant allele, would represent a dominant trait, the recessive trait would be completely masked as if the allele for the recessive allele does not exist.

Hence, if the one of the parents has dominant alleles only, the progeny would also have dominant traits.