in the manual you can find :
Operators Operators join together the other items within the expression. They include for example -o (meaning logical OR) and -a (meaning logical AND). Where an operator is missing, -a is assumed.
So litterally \( -perm -0002 -a ! -perm -1000 \) means :
perm = 0002 and not perm = 1000
perm = 0002 means writeable for Others perm = 1000 means sticky bit is set.
So this expression search for file writable for Other and without sticky bit sets.
Looking for directory is done with -type d d means directory so find look after object of type directory
from the find manual, -perm has several forms :
-perms 0002 will match all files with this exact permission setting
-perms -0002 will match all files where this right bit is setup, (which means 0772,1752...whatever combination if the file is writeble for others)