It's a login control that's used to display the name of the current Logged in user. Basicly it displays the value of System.Web.UI.Page.User.Identity.Name ( or simply User.Identity.Name),and it will only displayed for the logged in user , and it renders the User Name inside the <span> html tag.
LoginName has FormatString property which allows the developer to display a formatted text instead of just displaying the logged in user name. For example setting that property to"Hello, {0} " will displays "Hello,John " when "John" logged in.Basicly it will replace the "{0}" token with the current logged in user name.
Links:
How to: Display the Name of the Current User
LoginName Class
Walkthrough: Managing Web Site Users with Roles
