Modes
When LaTeX is processing your input text, it is always in one of three modes:
Paragraph mode
Math mode
Left-to-right mode, called LR mode for short
Mode changes occur only when entering or leaving an environment, or when LaTeX is processing the argument of certain text-producing commands.
Paragraph mode is the most common; it’s the one LaTeX is in when processing ordinary text. In this mode, LaTeX breaks the input text into lines and breaks the lines into pages.
LaTeX is in math mode when it’s generating a mathematical formula, either displayed math or within a line.
In LR mode, as in paragraph mode, LaTeX considers the output that it produces to be a string of words with spaces between them. However, unlike paragraph mode, LaTeX keeps going from left to right; it never starts a new line in LR mode. Even if you put a hundred words into an \mbox, LaTeX would keep typesetting them from left to right inside a single box (and then most likely complain because the resulting box was too wide to fit on the line). LaTeX is in LR mode when it starts making a box with an \mbox command. You can get it to enter a different mode inside the box—for example, you can make it enter math mode to put a formula in the box.
There are also several text-producing commands and environments for making a box that put LaTeX into paragraph mode. The box made 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” (no page breaks). Its normal paragraph mode, which it starts out in, is called “outer paragraph mode”.