What is the meaning of the ${0##…} syntax with variable, braces and hash character in bash?

See the section on Substring removal on the parameter expansion page of the bash-hackers’ wiki:

${PARAMETER#PATTERN} and ${PARAMETER##PATTERN}

This form is to remove the described pattern trying to match it from the beginning of the string. The operator # will try to remove the shortest text matching the pattern, while ## tries to do it with the longest text matching.

Example string (just a quote from a big man):

MYSTRING="Be liberal in what you accept, and conservative in what you send"

Syntax	Result
${MYSTRING#*in}	Be liberal in what you accept, and conservative in what you send.
${MYSTRING##*in}	Be liberal in what you accept, and conservative in what you send.