LaTeX is in paragraph mode when processing ordinary text. In that mode, LaTeX breaks your text into lines and breaks the lines into pages.
There are also several text-producing commands and environments for making a box that put LaTeX in paragraph mode. The box make by one of these commands or environments will be called a parbox. When LaTeX is in paragraph mode while making a box, it is said to be in inner paragraph mode, as distinguished from ordinary, or outer paragraph mode.