A genetic variant is a difference in the DNA sequence between individuals. Not all DNA codes for amino acids. Non-coding DNA lies in front of a gene, and this is where RNA polymerase binds to start transcription. A variant here can change how well RNA polymerase binds.
If the variant makes binding stronger, more mRNA is made, so more protein is produced. If it makes binding weaker, less mRNA is made, so less protein is produced. The amino acid sequence of the protein is unchanged, so each protein molecule is normal. What changes is the quantity of protein.
The amount of a protein can affect the phenotype, which is the observable characteristics of an organism. For example, imagine a gene for an enzyme that makes a pigment. A variant that weakens the binding of RNA polymerase means less enzyme, less pigment and a paler colour.