A functional group is a common group of atoms within a molecule (e.g. -Cl or -CO2H) and typically dictate or define reactivity, physical properties, and other traits of organic molecules. Similar functional groups in different molecules typically react in similar ways when subjected to a particular set of reaction conditions.
As your understanding of organic chemistry unfolds, take notice that the reactions occur directly at or immediately adjacent to many functional groups. Therefore, recognizing the functional groups within molecules is the key to recognizing the type of possible reactions that may occur.
Below is a list of functional groups you will encounter throughout your study of organic chemistry. The sooner you commit them to memory the better, as it is inevitable that you will learn them all eventually.