The simplest explanation usually for how alleles are either recessive or dominant is based on whether the protein they express has a higher than average function (gain of function) or lower than average function (loss of function).

Think about it through the lens of genetic disease. Oftentimes dominant genes are gain of function mutations. In Huntington’s disease, patients express a version of the protein huntingtin that is toxic to neurons and causes the condition. If you have two copies of alleles for huntingtin, but only one of them makes a toxic protein, you’d still have the toxic effect even though it represents only half of the expressed protein. That’s because this toxic effect is a “gain of function.” That’s what makes this allele dominant.

On the other hand, cystic fibrosis is a recessive disease. The gene for cystic fibrosis encodes a protein that transports sodium across cell membranes. Defects in this gene, called CFTR, can cause non-functional protein to be expressed and decrease the transport of sodium leading to a whole bunch of systemic effects. This is a loss of function. However, if you only have one mutant copy of the allele, then the other allele expresses a functional protein that can still do what the gene is supposed to do. This makes the disease recessive, because you need two “broken” alleles for a complete loss of this protein function.

Edit: punctuation