Short answers, pulled from the story.
Heredity, also called inheritance or biological inheritance, is the passing on of traits from parents to their offspring. It occurs through asexual or sexual reproduction, with the offspring acquiring the genetic information of their parents. The study of heredity in biology is genetics.
The genotype is the complete set of genes within an organism's genome, while the phenotype is the complete set of observable traits of an organism's structure and behavior. The phenotype arises from the interaction of the genotype with the environment, which is why traits like a suntan are not inherited.
Heritable traits are passed via DNA, a long polymer that incorporates four types of interchangeable bases. The sequence of those bases specifies the genetic information, and before a cell divides through mitosis the DNA is copied so each new cell inherits the sequence. A portion of DNA that specifies a single functional unit is a gene.
When Charles Darwin proposed his theory of evolution in 1859, it lacked an underlying mechanism for heredity. He relied on blending inheritance, which would push a population toward uniformity in a few generations and remove the variation that natural selection needs, leading him to adopt some Lamarckian ideas in later work.
Gregor Mendel was a Moravian monk who published his work on pea plants in 1865, introducing the idea of particulate inheritance of genes. His work was not widely known and was rediscovered in 1900, and his pea plant demonstration became the foundation of the study of Mendelian Traits.
Epigenetic inheritance covers heritable changes that cannot be explained by the direct agency of the DNA molecule. Discovered examples at the organismic level include DNA methylation marking chromatin, self-sustaining metabolic loops, gene silencing by RNA interference, and the three dimensional conformation of proteins such as prions.
An allele is dominant if it is always expressed in an organism's phenotype when at least one copy is present, as with the allele G for green pods in peas. A recessive allele, such as g for yellow pods, only shows its effect when present in both chromosomes as the homozygote gg.