Time to put your understanding of Gmail onto its head, especially if you're new to it and coming from a different email system. Let's dive right in.
Gmail is a database, meaning you have a mass of emails and can search and organize them in different ways. Unlike in Outlook or Notes, where you can shift discreet documents around, Gmail uses a big pool of emails that you can tag or categorize. This metaphor is key to understanding how Gmail works - abandon all thoughts about folders and buckets:
Emails never move. Instead of putting emails into folders, you are labeling them differently.
Gmail is a big pool of emails. You can categorize the emails in different ways - they never change place.
Since Gmail is a sea of emails, how can there be an inbox? There can't. Then ... if you don't have an inbox, what is permanently overflowing and eating your Fridays?
Your inbox is a filter. When a new email arrives, it is stored along with your emails, but Gmail sticks the label "inbox" onto it so you can find it easier (sometimes you can see that label!). I'll show you what it looks like in a bit. It's important to notice that incoming emails are in no special place, they are merely marked as "inbox".
Just as the inbox is a clever illusion, so are your folders.
What then is "the archive"?
For many of us, an archive is a separate place where content gets stored permanently. What goes in the archive tends to get forgotten. It is a place apart from the work desk, the day-to-day work.
Such a place exists in Outlook and in Notes, in the form of a separate "mail file". You can pack old email into archives, store them somewhere else and access when needed. Gmail doesn't work like that. It's all one.
You would expect to have an "archive" you could open, but that does not exist. Instead, Gmail has a something called "all mail" that the truly brave can look at. It contains - surprise - all mail, like an X-ray through your email life. Everything you have sent, everything you have received, everything you have put a label on (remember, they aren't folders). Even emails still in the inbox are there - that's why it's not called "The Archive".
Archive in Gmail is not a place, but a verb. It means "remove the inbox label". There is even an opposite, called "Move to inbox". That's better, but also a misnomer, because the email does not get moved. The action should be called "hide from inbox" and "show in inbox" - or even better, "Done". That's what Google Inbox called it.
Let's look at "All mail" (above) to see it all come to light:
This email is in the inbox. When you are in any view but the inbox, the Inbox label is revealed.
This email is in the inbox, too (it's got the label!). When you opened your inbox on this account, you would see emails 1+2, nothing else (Inbox zero is very much possible). This email also has the label Projects/ProjectX - to illustrate that labels are not folders.
This email is both in Projects and in the sub-label Project X. That is perfectly possible, because, you guessed it: Gmail uses labels, not folders.
This email is both in Project X and Project Y. This fact should not shock you at this point.
This email is starred. If you now think that starring and labeling are very similar, you are right.
This email has been auto-labeled as Promotions. Other message categories are social, updates and forums. I don't use them. Are these built-in categories like Inbox? Yes! Like labels? Quite so!
Contacts are not clustered in "groups", those have recently been renamed to "labels". Sounds familiar?
Some of these features may not translate exactly into all email clients, notably iOS mail. This might be one more reason to use the Gmail client on your iPhone.
I hope this gives you the confidence to archive fearlessly. If you are confident in Gmail's search, it should also free you from the need to create folders. Thanks for reading, and onward into an easier future with better metaphors!