In the Western European tradition, text runs from left-to-right (LTR) across the page, with lines stacked from top-to-bottom (TTB) down the page
Arabic, Persian, Hebrew and related middle Eastern systems have a reversal of the line direction, with text running from right-to-left (RTL) across the page. The lines still read from the top of the page down:
These two systems reverse the line direction but nothing else: handling both is therefore referred to as 'bidirection' work (LTR and RTL).
In writing systems from the far East, 'lines' of text run from the top of the page to the bottom. Lines can then be stacked next to each other either left-to-right
(Chinese, Japanese, Korean, ...) or right-to-left
(Mongolian). As these break out of the model used by European and middle Eastern traditions, these add a multiple' nature to the direction of text.
The TeX--XeT model currently implemented in pdfTeX and XeTeX is currently limited to handling LTR/RTL only, while the Omega-derived model in LuaTeX can also handle the far Eastern top-to-bottom cases. However, even that model is not perfect. John Plaice talked about improving handling for all of these cases in a simple way at TUG 2013: his article in TUGboat is available currently only to TUG members.