Aside from Priority Inbox, there are two other ways to manage this situation. One is by using the search bar and the other is with the use of filters.
Let us start with the search bar. Launch your favorite browser and sign-in to your Gmail account. On the search bar, type "before: 2010/06/01" (translating to June 01, 2010). Any date will do here as long as the format is yyyy/mm/dd. All that is left is to press the Search button.
Select the mails you wish to archive, and click on Archive. You will be getting a screenshot just like the one above.
Gmail seemed to have noticed that I ticked all mails that fall into the search criteria "before: 2010/06/01". And presented me with another option -- to select all messages that match the search. Just like below.
I clicked that link and archived all messages before June 1, 2010. Once you click Archive, wait for a minute or two for Gmail to process your request. Once its done, your Inbox will be quite easier to handle and loads a bit faster too. Quick and easy.
The next method is though the use of filters. Next to the search bar is the search button for mail and web. Then next to those in fine font is Create a filter. Fill out the field "Has the words:" with "before: 2010/06/01". Again, this could be another date but has to conform to the format yyyy/mm/dd, like below. Then click Next Step.
Next, tick Skip the Inbox (Archive it) and below it, also tick Also apply filter to XXXX conversations below. The filter will take a minute or two to execute, and once done you can delete the filter.
Just keep in mind that this is not a destructive process -- meaning your mails were not deleted and are still intact. You can still access them under All Mail or search for them on the search bar. What the procedures above did was to archive them from the inbox.
