very often in Internet I see links like this:
www.abcde.com/~main/material/hello
and this part ~main/material/hello is grey, if I remove hello I receive access forbidden, can somebody explain, what is this system, and is it possible receive access?
Directory listing is disallowed on www.abcde.com/~main/material/, but you have access to it's content.
They've configured the web server to only allow access to certain areas. You won't be able to receive access to it.
The tilde (~) is *nix convention for a user's home directory. Using it in the URL tells an appropriately-configured web server to look in a directory in the user's home directory for the files to show via the web server.
Depends on the web server. On Apache this can be done with
Options -Indexes
what do you mean it is grey? the link text on a page? That can be any colour that the page owner wants, but I don't remember seeing a grey link.
What happens if you type www.abcde.com/~main/material/hello directly into the browser's address window?
If you remove "hello" and receive access forbidden it is because there is no public access to www.abcde.com/~main/materia - give up, you will never access that without a password.