Archiving is important if you use IMAP email (most of us do) to prevent email storage from reaching its limit. If it fills up, you'll stop receiving mail.
Here's how to archive email by year, using Apple Mail. This will pull mail from your provider and copy it to your computer in an archive folder. Doing so will allow you to view it on this Mac only and not multiple devices, so archive outdated email only.
Create a Mailbox for the Archived Mail
Select "New Mailbox..." from the Mailbox menu. Set the Location to "On My Mac" and give it a name. For this example, we'll call it "2012 Archive." Click "OK."
Create a Smart Mailbox to View and Select Mail from 2012
Select "New Smart Mailbox..." from the Mailbox menu. Enter a name such as "2012" and select "Date Received" and "is in the date range" and "1/1/2012 to 12/31/2012." Check the box to include messages from Sent. Click "OK."
Move the Messages
The Smart Mailbox appears in the list on the left. Select it and the messages from 2012 appear to the right. Now use Command-A to select all the messages. Drag the messages to the 2012 Archive Folder. Once you release the mouse, there may be a significant delay to move the messages, so be patient.
You've just archived all of your messages from 2012.
If you'd like to remove mail from Apple Mail entirely, select a folder (for example the archive folder) and select "Export Mailbox" from the Mailbox Menu. This will allow you to save it to your computer in a form that can later be imported again if necessary. You can then safely delete that Folder.