If you do a google image search you will probably find a diagram that will doubtlessly better convey the following explanation:
It is generally cloud free in the 'eye' of a typhoon as a result of the convective structure of the storm. The tubular wall of cloud lining the eye of the storm is where windspeed is at its greatest and also the position where air rises most rapidly; this could be understood as resulting from the fact that the [I]pressure gradient [I] is greatest there (i.e. the isobars are really close together there).
The air surrounding the eye rises and builds substantial cells. However, eventually the air reaches the tropopause and can't continue to rise because of the levelling off of the [I]temperature gradient[I]. When the air reaches the tropopause it is therefore forced to move laterally - most of it moves outwards toward the extremity of the storm. [U]However[U] some of it moves laterally toward the centre. So all this air that converges at the centre of the storm up at the tropopause has to go somewhere: It has 'no choice' but to DESCEND.
As I'm sure you're aware clouds most commonly form when air rises, cools and temperature and dewpoints meet causing condensation of water content to form water droplets.
When air DESCENDS the opposite generally occurs: the air warms, water droplets become vapour and hence the air is 'clear' or 'cloud free'. Hence the gently descending air at the central 'eye' of a typhoon is cloud free.