What happens to characteristics found in one generation of a species as it reproduces and has offspring?
Genetic characteristics are inherited by offspring but acquired characters are not.
Acquired characteristics are not inherited from parents. These are acquired during life time, caused by various factors, like disease/injury/environment/habit, etc.
Then there are human tribes who deliberately attempt to modify their body parts, such as chinese women who constrict development of feet. But such characteristics are never inherited by the progeny.
Any characteristic, controlled by gene would be inherited. When organisms undertake sexual reproduction, new recombination of characteristics also appear in the progeny.
Sometimes an organism may develop mutation in germ cells. In such cases, new characteristic may appear in progeny due to the mutation it has inherited.
Note: while most acquired characteristics are not inherited due to the mechanisms of inheritance, there are exceptions to this. More information can be found in the epigenetics section of Socratic.