Is it the "end of option" I am used to see in bash (and if yes, why do we use it) or is it a Git notation for the Index or the HEAD?
-- separates the paths from the other options. From the documentation:
git checkout [-f|--ours|--theirs|-m|--conflict=<style>] [<tree-ish>] [--] <paths>...
If this notation didn't exist the following two commands would be ambiguous:
git checkout <tree-ish> <path1> <path2> git checkout <path1> <path2> <path3>
-- notation it is clear which is meant:
git checkout <tree-ish> -- <path1> <path2> git checkout -- <path1> <path2> <path3>
The documentation I linked to above includes an example of when you might need it:
$ git checkout hello.c
If you have an unfortunate branch that is named hello.c, this step would be confused as an instruction to switch to that branch. You should instead write:
$ git checkout -- hello.c