19th-century Austrian monk Gregor Mendel is famed as the father of modern genetics. When his experiments with pea plants were rediscovered after his death, they proved revolutionary. The same principles that Mendel discovered remain central to genetics today. Nonetheless, there are many traits that are not inherited in the manner described by Mendel. Polygenic traits are an especially important example.
Mendelian traits are determined by a single gene and inherited in a simple fashion that follows the laws of inheritance described by Mendel. If each parent is heterozygous (has two different variants of a given gene), 3/4 of their progeny will have the "dominant" version of the trait, while 1/4 will have the "recessive" version. The parents may also be homozygous, in which case they have two identical copies of the gene. If one parent is homozygous for the dominant version of the gene while the other parent is homozygous for the recessive form, all their progeny would be heterozygous.
Many important genetic disorders are associated with a single gene and thus exhibit Mendelian patterns of inheritance. Cystic fibrosis is a well-known example. The gene involved with this disorder has a "normal" variant and another variant that causes cystic fibrosis. Cystic fibrosis, however, is a recessive trait, so you have to inherit two copies of the disease-causing variant to have the disorder -- one copy from mom and one from dad. The ratio of children who have the disorder to children who do not can be predicted based on the variants that the parents have and the simple ratios that Mendel used to predict inheritance in his pea plants.
Polygenic traits are much more complex than Mendelian traits. Rather than being shaped by a single gene alone, a polygenic trait is influenced by multiple genes. In humans, eye color and skin color are two of the most well-known examples. There isn't a single gene for darker brown or lighter white skin; rather, there are multiple genes, and the combination you inherit determines your skin color. Many different combinations are possible, so humans exhibit many different shades of skin color.
Predicting how a Mendelian trait will be inherited is fairly straightforward. Predicting how a polygenic trait will be inherited, by contrast, is much more difficult. With skin color, for example, if both parents have different combinations of genes, there are many possible outcomes that might turn up in their children. While the individual genes all exhibit Mendelian patterns of inheritance, the trait itself does not, because so many different genes are involved in shaping it.