Multiple alleles is a type of non-Mendelian inheritance pattern that involves more than just the typical two alleles that usually code for a certain characteristic in a species. With multiple alleles, that means there is more than two phenotypes available depending on the dominant or recessive alleles that are available in the trait and the dominance pattern the individual alleles follow when combined together.
Gregor Mendel only studied traits in his pea plants that showed simple or complete dominance and had only two alleles that could contribute to any one trait the plant showed. It wasn't until later that it was discovered that some traits can have more than two alleles that code for their phenotypes. This allowed many more phenotypes to be visible for any given trait while still following Mendel's Laws of Inheritance.
Most of the time, when multiple alleles come into play for a trait, there is a mix of types of dominance patterns that occur. Sometimes, one of the alleles is completely recessive to the others and will be masked by any of those that are dominant to it. Other alleles may be co-dominant together and show their traits equally in the phenotype of the individual. There are also some cases where some alleles exhibit incomplete dominance when put together in the genotype. An individual with this type of inheritance connected to its multiple alleles will show a blended phenotype that mixes both of the alleles' traits together.
The human ABO blood type is a good example of multiple alleles. Humans can have red blood cells that are of type A (IA), type B (IB), or type O (i). These three different alleles can be combined in different ways following Mendel's Laws of Inheritance. The resulting genotypes make either type A, type B, type AB, or type O blood. Type A blood is a combination of either two A alleles (IA IA) or one A allele and one O allele (IAi). Similarly, type B blood is coded for by either two B alleles (IB IB) or one B allele and one O allele (IBi). Type O blood can only be obtained with two recessive O alleles (ii). These are all examples of simple or complete dominance.
Type AB blood is an example of co-dominance. The A allele and the B allele are equal in their dominance and will be expressed equally if they are paired together into the genotype IA IB. Neither the A allele or the B allele is dominant over each other, so each type is expressed equally in the phenotype giving the human an AB blood type.