For those (such as myself) with poor visualization abilities who have trouble following teleny's excellent writeup, may I present an ASCII sketch:
_.-"-._
.' `.
/ A S I A \
| |
Black Sea +------J------+ Red Sea
| EUR | AFR |
\ OPE | ICA /
`._ | _.'
`-+-'
M
e
d
i
t
e
r
r
a
n
e
a
n
(Where the J in the centre is Jerusalem.)
T-O maps are interesting because they demonstrate how much the design of contemporary maps is arbitrary:
Firstly, as geographic information decreased proportionally to the distance from the (Arabian) mapmakers, it was natural to put the most important local city, Jerusalem, in the centre*. A similar bias may be evident in the contemporary popularity of the Mercator projection, which enlarges the temperate areas of importance to Western civilization, rather than the supposedly egalitarian Peters projection.
Modern cartography is driven first and foremost by the power of maps to control resources. Since this ability was not fully realised when T-O maps were produced, there is less emphasis on spatial correctness. (Plus, without the ability to calculate longitude, maps aren't all that useful for navigation.) Instead, these maps emphasise logical ordering which is of greater importance for general and political education. (Who is next to whom is more important than the abstract absolute position of any particular geographic entity.)
Finally, as compasses were not yet widely available, the contemporary habit of North-oriented maps is absent. Instead, mythology concerning what lay beyond the edge of the maps dictated the orientation.
* Interestingly enough, Avalon-Hill's History of the World game also puts the Middle East at the centre of the board and uses a projection that compresses space proportional to the distance from the edge. Presumably this is because the Middle East is not only the birthplace of civilization but also decisive events in the history of the world tend to occur closer to there than any other point.