An additional, not immediately obvious meaning or association attached to the main meaning of a word or phrase. Connotations can be reflections of specific cultural or historical context, thinking patterns, value judgements, etc. In German: die Konnotation / die Nebenbedeutung.
The connotations of a word or phrase are like resonances or "vibes". In contrast,
denotation gives you the definition of a word as you would find it in a dictionary. Connotations are acquired over time through usage. Choosing a word that carries undesired connotations may get you into hot water with native speakers. For example,
Führer literally means leader but carries the historical baggage of being Hitler's official title (hence,
Anführer would usually be better choices.) Connotation is independent of inflection, which is reserved to speech.