The distinction between necessary and sufficient is important in logic and rhetoric (and therefore, we would like to believe, in debate and politics), although it is often ignored by those who speak to the masses.
Something is necessary if X cannot be achieved without it. Something is sufficient if something can be achieved with X, but might also be achieved without X.
A classic reminder of the difference is "a sledgehammer is sufficient to drive a nail into a board, but it is not necessary".
Aside from the common rhetorical error of calling sufficient things necessary ("It is necessary to reduce government expenditures in order to reduce the national deficit"), other common fallacies include identifying one necessary and/or sufficient condition but ignoring others ("If you you want to cut taxes, vote for me" [... and reduce services]) and assuming that there is only one sufficient and/or necessary condition ("Our current gun control policy is not sufficient to reduce crime, therefore we must strengthen it"...[or find another way to lower crime rates]).
The ideas represented by necessary and sufficient are very frequently an important part of the issues presented in public debate, but because people find these terms vaguely confusing they are often replaced by simpler words -- "we need", "it works -- and sometimes dropped altogether. When listening to a logical argument you should be ready to rephrase the argument using these terms, and to question any argument that falls apart when rephrased with a more strict formulation.