Mendel's laws of inheritance describe how traits are passed from parents to offspring, based on his experiments with garden peas. He conducted monohybrid and dihybrid crosses, leading to the formulation of three key laws: the law of dominance, law of segregation, and law of independent assortment. These laws explain genetic traits' inheritance patterns, where dominant traits overshadow recessive ones, and how alleles segregate and assort independently during gamete formation.