To connote means to suggest or imply something beyond a word's literal definition. Words carry feelings and associations along with their basic meanings, and when a word connotes something, it brings those extra layers with it.

Consider home and house. Both refer to a place where people live, but home connotes warmth, family, and belonging, while house simply means the building. Or think about cheap versus inexpensive: both mean something doesn't cost much, but cheap sometimes connotes low quality, while inexpensive sounds perfectly respectable.

The noun form is connotation. You might say that the word “childish” has negative connotations (suggesting immaturity and silliness), while “childlike” has positive connotations (suggesting innocence and wonder).

Good writers pay attention to what words connote, choosing carefully between synonyms that denote the same thing but feel quite different.