Mendel's law of independent assortment states that the genes for different traits are passed to offspring separately. In Mendel's original experiments with pea plants, this meant that plants with heterozygous genes for two different traits would pass the alleles for each gene separately.
Mendel determined the law of independent assortment when he studied the genetics of pea plants. By crossing plants that were heterozygous for particular traits, Mendel was able to trace different alleles passing through the generations of offspring based on the ratios of offspring that had particular traits.
In the cases that Mendel studied, the pea plant traits had two types or alleles. The dominant allele determines the trait if it is present, even if the other allele is recessive. The recessive allele can only be viewed in the offspring if both chromosomes of the plant have the recessive allele.
If independent assortment was not the case, then Mendel would have seen the traits sort together in the offspring of crosses between two plants that were hybrid for two different traits. In other words, if one of the parents carried a dominant allele for two traits, then any offspring that inherited the dominant allele for the first trait must also have the dominant allele for the second. However, what Mendel observed was that this was not the case; offspring could inherit either the dominant or recessive alleles regardless of which allele was inherited with regard to the other trait.