The sessions plugin is a very low level plugin used to link clients with the server. That way we can save certain client's information such as options they select for a better browsing (i.e. their timezone to get dates formatted as expected for their location.)
Sessions are used with anonymous users as well as registered and logged in users.
A session is a pair of numbers assigned to each user. The numbers change from time to time to avoid session hijacking (a potential security issue).
The editor plugin, among others, also makes use of sessions. This is useful to prevent basic web spam (i.e. a form where robots can just send a POST with data to be saved in you website database.) Having a session at least forces the robots to first access your website to gain knowledge of the session assigned to that form. Without it, the form submission will always fail.