Genetic dominant means and why it makes a difference in crossbreeding animal

Genetically dominant means that the trait will always be dominant to the genetically recessive trait as long as the allele for that trait is present. 

Let's say you have an R allele that codes for a brown coat and an r allele that codes for a white coat. Say the R allele is genetically dominant to the r allele. 

If you have an animal with the genotype RR or Rr, it will show a brown coat because the genetically dominant R allele is present.

Only if the animal as a rr genotype will the white coat show because the genetically dominant R allele isn't present.

When you crossbreed, genetic dominance can be important because it can increase the chances you'll have more diverse offspring with increased chance of survival since the dominant traits, if favorable, will always show for a trait.