An allele that varies in it sequence from what is considered the reference or canonical sequence at that location.
Note that what is considered the 'reference' vs. 'variant' sequence at a given locus may be context-dependent - so being 'variant' is more a role played in a particular situation. A 'variant allele' contains a 'sequence alteration', or is itself a 'sequence alteration', that makes it vary_with some other allele to which it is being compared. But in any comparison of alternative sequences at a particular genomic location, the choice of a 'reference' vs the 'variant' is context-dependent - as comparisons in other contexts might consider a different feature to be the reference. So being 'variant' is more a role played in a particular situation - as an allele that is variant in one context/analysis may be considered reference in another. A variant allele can be variant along its entire extent, in which case it is considered a 'sequence alteration', or it can span a broader extent of sequence contains sequence alteration(s) as part. And example of the former is a SNP, and an example of the latter is a variant gene allele that contains one or more point mutations in its sequence.
The use of the descriptor 'variant' here is consistent with naming recommendations from the ACMG Guidelines paper here: PMID:25741868. Generally, the descriptive labels chosen for subtypes of variant allele conform these recommendations as well, where 'variant' is used to cover mutant and polymorphic alleles.