LightDM is a Display Manager. It is a long running process (daemon) that ensures that your graphical display is set up correctly.
The LightDM daemon spawns and manages two types of processes:
Display Servers - a process that combines graphical output from one or more process together to display on graphics hardware. Also provides input from mice / keyboards etc to the process. For example X is a display server.
Sessions - a session is a process that has access to the display server and allows the user to perform tasks. Often a session will be made up of a core component, the shell, that allows the user to run applications. Both the shell and the applications communicate with the display server.
Authentication is performed using PAM.
A greeter is a session that provides a mechanism for choosing and authentication users.
A user session allows a user to interact with their computer and run applications.
You can allow remote computers to connect to LightDM and start sessions.