What causes the dominance or recessiveness of the gene? How does this mechanism work?

one of the alleles can suppress the expression of the other, or the translate of the dominant one makes an immeasurably greater contribution to the phenotype than the translate of the recessive one.

All phenotypic manifestations of genes, as well as their interactions with each other, are determined by the proteins that they encode. What we call the dominance or recessiveness of genes is nothing more than the contribution of their products to the formation of the whole organism.

Easier to explain with a simplified example: the hair color gene encodes an enzyme that ensures the accumulation of pigment in them. There are two variants of a gene (two alleles) - normal and defective. The first, getting into a homozygous state, will ensure the normal accumulation of pigment and, accordingly, black hair color, the second is not capable of accumulating it, therefore the hair will be discolored. Being in a heterozygous state, each allele reproduces its own enzyme, however, the pigment will accumulate due to the presence of the first allele and the hair will acquire color (perhaps not black, since we will already talk about incomplete dominance). In this case, what do we say that the first allele dominates the second

This is a very simplified model, but it shows that at the biochemical level there is no particular difference between dominant and recessive genes, we can talk about their effect only when in general, we look at the phenotype