A monogenic trait is a characteristic that is produced by a single gene or a single allele. A gene is a DNA segment that is responsible for physical traits and the phenotype of an organism. An allele is one of a pair of genes on a chromosome - the pair controls the same trait.
An example of a monogenic trait is eye color or the ability to roll your tongue. A polygenic trait is a characteristic controlled by two or more genes that are located at different areas on different chromosomes.
Examples of polygenic traits include height and weight - many genes are involved in the expression of these traits.