What is a `##` means in bash variable substitution `${}`?

I am learning the bash script materials on http://www.tldp.org/LDP/abs/html/index.html and stuck in the Example 7-7:

http://tldp.org/LDP/abs/html/comparison-ops.html#EX14

There is an ${filename##*.} != "gz", this probably means that the $filename does not end with .gz, but I do not know the meaning of ## here. Could anyone help me?

Thanks!