A biallelic site is a specific locus in a genome that contains two observed alleles, counting the reference as one, and therefore allowing for one variant allele. In practical terms, this is what you would call a site where, across multiple samples in a cohort, you have evidence for a single non-reference allele. Shown below is a toy example in which the consensus sequence for samples 1-3 have a deletion at position 7. Sample 4 matches the reference. This is considered a biallelic site because there are only two possible alleles-- a deletion, or the reference allele G.

           1 2 3 4 5 6 7 8 9
Reference: A T A T A T G C G
Sample 1 : A T A T A T - C G
Sample 2 : A T A T A T - C G
Sample 3 : A T A T A T - C G
Sample 4 : A T A T A T G C G

A multiallelic site is a specific locus in a genome that contains three or more observed alleles, again counting the reference as one, and therefore allowing for two or more variant alleles. This is what you would call a site where, across multiple samples in a cohort, you see evidence for two or more non-reference alleles. Show below is a toy example in which the consensus sequences for samples 1-3 have a deletion or a SNP at the 7th position. Sample 4 matches the reference. This is considered a multiallelic site because there are four possible alleles-- a deletion, the reference allele G, a C (SNP), or a T (SNP). True multiallelic sites are not observed very frequently unless you look at very large cohorts, so they are often taken as a sign of a noisy region where artifacts are likely.

           1 2 3 4 5 6 7 8 9
Reference: A T A T A T G C G
Sample 1 : A T A T A T - C G
Sample 2 : A T A T A T C C G
Sample 3 : A T A T A T T C G
Sample 4 : A T A T A T G C G

To learn more about multiallelic sites and their frequency in natural populations, see this article by Heng Li.