Definition of Functional Group
The definition of a functional group is structural classes of molecules that have similar properties and tend to react in fairly predictable ways.
To speak about molecules generally, your textbook probably uses R groups, which is another way of saying “any carbon chain can be added here.”
Your book also probably uses X’s as well, which generally represent the halogens (F, Cl, Br, and I), a column of reactive elements that are frequently used in organic chemistry.
Your textbook should have a good table summarizing the functional groups. Some professors make students memorize these early in first semester while others don’t. Each individual functional group will have its own chapter about its structure, properties, and reactivity, generally in the 2nd semester. At this point in the course, our discussion of functional groups is limited to a simple introduction.