Notifications are part of your Inbox. They are automatically sent to everyone on ROBLOX. You can't archive the notifications, because they automatically delete themselves after a given period of time. These notifications usually notify you about recent updates, which go anywhere from critical bug patches to advertisements about the latest gear. Notifications are usually sent by admins, usually Telamon or reesemcblox.
Notifications have a relatively limited role in ROBLOX's site design as of August 2012, which implies that it is subject to more updates that build atop the existing framework.