When you archive a message in Gmail, it disappears from your inbox and moves to All Mail. You can find the All Mail section when you open the 'More' section and All Mail should be lumped in with chats, spam and trash.

How do I find my archived emails?

To see archived emails on your Android device —> open your Gmail app —> click on the hamburger icon on top left, and then click on All Mail label. Here you will see all archived emails as shown in the screenshot below.

What happens to emails that are archived?

When you archive an email, you file it away for future reference. And if someone responds to an email that was archived, it will reappear in your Inbox. Archiving is the best solution for emails that you want out of the inbox but for which there's a good chance you might need them later.