Every gene contains the information to express a particular trait.

In a diploid organism there are two copies of each gene i.e. as a pair of alleles.

These two alleles need not always be identical as in a heterozygote.

One of them may be different due to some changes that it has undergone which modifies the information that particular allele contains.

Let's take an example of a gene that contains the information for producing an enzyme.

Now there are two copies of this gene, the two allelic forms.

Let us assume that the normal allele produces the normal enzyme that is needed for the transformation of a substrate $S.$

Theoretically the modified allele could be responsible for production of :$ (i)$ the normal/less efficient enzyme or $(ii)$ a non-functional enzyme or $(iii)$ no enzyme at all.

In the first case, the modified allele is equivalent to the unmodified allele i.e. it will produce the same phenotype/trait i.e. result in the transformation of substrate $S$.

Such equivalent allele pairs are very common.

But, if the allele produces a non-functional enzyme or no enzyme, the phenotype may be effected.

The phenotype/trait will only be dependent on the functioning of the unmodified allele.

The unmodified (functioning) allele, which represents the original phenotype is the dominant allele and the modified allele is generally the recessive allele.

Hence in the example above the recessive trait is seen due to non-functional enzyme or because no enzyme is produced.