Short definition: The frequency of the less common allele at a genetic locus in a given population or dataset. For a biallelic site with allele frequencies p and q, MAF = min(p, q). Reported as a fraction or percentage.
"Minor" specifies the less common allele, ensuring the metric is bounded in [0, 0.5] for biallelic variants and is comparable across studies and populations even when the reference/alt designation differs.
By definition, for biallelic sites MAF = min(p, q) and for multiallelic sites it is the frequency of the second most common allele; therefore MAF ≤ 0.5. The "reference" allele is not guaranteed to be the major allele in a population.
Some databases/browsers report the alternate allele frequency (relative to the reference allele), which can be close to 1.0 if the reference allele is rare or absent in that population. This does not imply MAF is 1.0; it reflects that the alternate allele is common while the reference allele is rare. See NCBI Variation Viewer FAQ and gnomAD/ExAC notes.