Functional groups are specific groups of atoms within molecules that have very characteristic properties regardless of the other atoms present in a molecule. Functional groups focus attention on the important aspects of the structure of a molecule. Focusing on the functional groups in a molecule allows us to recognize patterns in the behavior of related compounds. The reactions and reactivity of organic compounds are often determined by the functional groups attached to the carbon chain of which they are a part.
Hydrogen (H) atoms form one single bond to another element. It must be to another element (and not to another hydrogen atom) because two hydrogen atoms linked together form a single molecule of hydrogen gas, H2.
Halogen atoms, that is atoms of fluorine (F), chlorine (Cl), bromine (Br), iodine (I) and, in theory, Astatine (At) also form only one single bond to another element. As for hydrogen, the bond must be to an atom of another element because two halogen atoms linked together form a single molecule of the gas of that element.
Oxygen (O) atoms form either two single bonds to other atoms OR one double bond. Oxygen atoms can form single or double bonds with other oxygen atoms but two oxygen atoms linked together by a double bond form a molecule of oxygen gas (O2), so when working-out or checking drawings of molecular structures in organic chemistry it is worth remembering that a double bond from an oxygen atom does not go to another oxygen atom, but usually to an atom of carbon.
Nitrogen (N) atoms form either three single bonds to other atoms (e.g. to two atoms of hydrogen and one of carbon in the case of amines) OR one single bond to another atom and one double bond to a different atom OR one triple bond to another atom. Similar to the cases for the elements mentioned above, when working-out or checking drawings of molecular structures in organic chemistry it is worth remembering that a triple bond from a nitrogen atom does not go to another nitrogen atom because two nitrogen atoms linked together by a triple bond form a singe molecule of nitrogen gas (N2). Triple bonds from nitrogen atoms in organic compounds are generally to carbon atoms (as in nitriles).
Carbon (C) atoms form four single bonds to other atoms or any combination of single, double, or triple bonds that can be represented by a total of 4 lines, where double bonds are represented by two lines between the same two atoms and triple bonds are represented by three lines between the same two atoms.