It removes everything up to the last wlan match in the $x variable.
asldkjflkasjdfljsdwlanalsdkjfkajsdflswlanasdlfaksdlfj
#                 ^^^^               ^^^^
#                     |                  |--->
#                     |                  ${x##*wlan}
#                     ${x#*wlan}
See an example:
$ x="hello1hello2hello3"
$ echo "${x##*hello}"  # with two ## it matches the longest matching pattern
3
$ echo "${x#*hello}"   # with one # it matches the shortest matching pattern
1hello2hello3
Graphically:
hello1hello2hello3
#                ^
#    ^           ${x##*hello}
#    ${x#*hello}
From Bash Reference Manual - 3.5.3 Shell Parameter Expansion:
${parameter##word}
The word is expanded to produce a pattern just as in filename
  expansion (see Filename Expansion). If the pattern matches the
  beginning of the expanded value of parameter, then the result of the
  expansion is the expanded value of parameter with the shortest
  matching pattern (the ‘#’ case) or the longest matching pattern (the
  ‘##’ case) deleted. If parameter is ‘@’ or ‘’, the pattern removal
  operation is applied to each positional parameter in turn, and the
  expansion is the resultant list. If parameter is an array variable
  subscripted with ‘@’ or ‘’, the pattern removal operation is applied
  to each member of the array in turn, and the expansion is the
  resultant list.