Organisms are able to produce exact copies of themselves due to - 

The basic event in reproduction is the creation of a DNA copy. With a series of chemical reactions, cells build copies of DNA. Once the cell is kept in the parent cells the copy is with the new cell which is formed. Hence, it is said that organisms create exact copies of themselves.

However, in the case of sexual reproduction, some variations occur during DNA copying, and hence, the copies will be similar.