Heredity is the scientific study of how traits are inherited. The scientific view of heredity has changed a great deal over the span of human history; the prevailing belief for many centuries was called the "inheritance of acquired characteristics", in which organisms could pass down traits they had acquired (e.g., susceptibility to an illness suffered earlier in life) to their offspring.
Acquired inheritance had its share of criticisms in the 19th Century and was particularly undermined by Mendel's two laws (1st law, 2nd law), which proposed that an organism's genes are determined completely by unalterable hereditary units (called alleles) that are passed from one generation to the next. Today, we know that Mendel's alleles are encoded by markers on chromosomes, although the modern model of heredity has gotten progressively more complicated, such as the discovery of polymorphic traits, which are represented by more than one different factor.
That having been said, studies today are re-opening the accepted maxim that acquired traits cannot be inherited, as the field of epigenetics expands the study of inheritance beyond simply analyzing nucleic acid primary structure. Specifically, methylated DNA can apparently be inherited, and methylation is a process that cells initiate to regulate their genes.