Function

What does this block do?

This block adds a login block to your page.
This block does allow you to login to your site from every page, by using the default concrete5 login.

basic function:

<login block> --> posting login details to /login --> /login will handle the login using the default (concrete) authentication type.

 

My block shows me a login form while logged in

Yes, this is correct.
The block will show you a login form when you are logged in, and can edit the page.
Normal logged in visitors of the page will not see the login block. 

We do show the block so you can find it again. When editing the page.
You can disable this by adding a custom template and changing line 7 from the template:

if (!$user->checkLogin() || $cp->canWrite()) {?>
into
if (!$user->checkLogin()) {?>