Fixity of Species refers to the set of beliefs derived from the ideas of Plato, Aristotle and Carolus Linnaeus which held that species have remained unchanged since their appearance on earth. This was later contradicted by the development of the Theory of Evolution.
The essential ideas behind Fixity of Species can be traced to classical philosophy. Plato's Theory of Forms drew a distinction between our material reality and a separate realm of Forms. These Forms are supposed to be eternal, ideal and abstract representations of things in our world. Our world contains only imperfect shadows of Forms. As such, the variation we see in things around us is unimportant since it is caused due to trivial imperfections. Aristotle applied Plato's idea to living things and stated that there are eternal ideal types for each species and since the creatures we see around us are imperfect manifestations, any variance among them is unimportant.
The above ideas were consolidated and formalized by Linnaeus' Typological Concept of Species in the 18th century. He stated that entire species could be represented by one ideal specimen, called the holotype. These eternal holotypes were created by God and have remained static ever since. Species were supposed to be discrete classes which remain eternally unchanged. This was widely accepted among European botanists and zoologists as it conformed to Christian beliefs about creation. These ideas were also backed by empirical evidence at the time. Joseph Kolreuter, for example, crossbred two groups of tobacco to create a new form but then obtained one of the parent types through repeated backcrosses.
Charles Darwin was trained to take the fixity of species for granted. However, after finding that he was unable to properly classify the wide range of bird species he had collected on his voyage on the HMS Beagle, he began to consider the idea that species could be transmuted to others. The rest is, of course, history.