Just delete everything until the last slash:
$ echo "blablabal/important" | sed 's:.*/::'
important
$ echo "blablabal/important" | sed 's:.*/::'
important
It also works with multiple slashes:
$ echo "blablabal/not/ver/interesting/important" | sed 's:.*/::'
important
$ echo "blablabal/not/ver/interesting/important" | sed 's:.*/::'
important