An organic molecule consists of carbon as a elementary atom. Thus, all molecules in which a carbon atom bonds to other atoms such as oxygen, hydrogen, nitrogen, another carbon atom etc. are considered as organic molecule.
For example -
Methane - Here, carbon atom is bonded to four hydrogen atoms
Methanol - Here, carbon is attached to three hydrogen atoms and one hydroxyl (OH) ion.
Organic matters are generally carbon compounds. Therefore, the organic molecules contain carbon. The main reason of the presence of carbon in the organic molecules is the catenation property of carbon.