In lotus notes, your e-mail database lives on the Domino server. If you have reason to access your e-mail while not connected to the server (as is the case with a notebook/laptop systyem or a remote office with limited connectivity), you will need to create a replica of your e-mail (and most likely your corporate address book as well). The replication process, as the name implies, creates an exact copy (using default settings) of your server database (e-mail or other) on your local drive (it replicates the database). You’ll need to re-replicate regularly to make sure that changes made locally are written to the server and server changes are written to your local copy.
Archiving is the preservation of certain data (e-mails over 30 days old for example) to a separate database, either on a server or (more likely) on the local drive. This reduces the size of the server based mail file (useful or necessary of you have quotas enabled).