functional group
A long hydrocarbon chain is chemically rather boring — it mostly just sits there. The interesting chemistry happens at special spots where an atom or small cluster of atoms breaks the monotony: a double bond, an OH, a C=O, an NH2. These reactive hot-spots are functional groups, and they are the single most powerful organizing idea in all of organic chemistry. Learn how one functional group behaves, and you understand that behaviour in millions of molecules that share it.
A functional group is a specific arrangement of atoms (often including oxygen, nitrogen, or a double or triple bond) that gives a molecule a characteristic and predictable set of reactions, largely independent of the carbon skeleton it rides on. Ethanol and octanol are different sizes, but both have an OH and both undergo the reactions of alcohols. Because of this, chemists classify the millions of organic compounds into a manageable number of compound classes — alcohols, ketones, carboxylic acids, amines, and so on — each defined by its functional group. The functional group is where electrons are unevenly distributed, where bonds are weaker or more polar, and so it is where nucleophiles, electrophiles, acids and bases come to do their work.
Thinking in functional groups is what turns organic chemistry from rote memorization into a system. You do not memorize every molecule; you learn the small repertoire of functional groups and how they react, then read a new molecule as a familiar skeleton decorated with one or more groups you already know. The whole later structure of an organic course — and of the fields in this glossary — is essentially a guided tour through the functional groups one class at a time.
The OH in ethanol (CH3CH2OH), in cetyl alcohol (a 16-carbon waxy solid), and in menthol all behave the same way — they form hydrogen bonds, can be oxidized, can be turned into esters — because they are the same hydroxyl functional group on different skeletons.
Same group, different skeletons, same chemistry — the core promise of the functional-group idea.
A functional group's reactivity is mostly local, but not entirely: nearby groups, conjugation and ring strain can modulate it, so the carbon skeleton is a backdrop, never wholly irrelevant.