What are dominant and recessive alleles?

Well firstly, alleles are different versions of genes. A dominant allele will show it's trait regardless of if the organism only has one copy of the allele (heterozygous). A recessive allele will show the effect only if two copies of the allele are present (homozygous)

If the two alleles are different, the plant is said to be a hybrid or heterogeneous for that traits. As Mendel noted, when both alleles are present, one allele masks or hides the other. The stronger allele is said to dominant, and the weaker allele that is masksed is said to be recessive.