One of the great benefits of using Gmail is we no longer have to worry about our inbox getting too large. Instead of having to spend time moving emails around, making the choice to delete them and hope you never need them again or leaving them to clog up your inbox, the Archive option allows you to quickly and easily remove emails from your inbox but still have them available should you need them at a later date.
The Archive button just removes the 'Inbox' label from an email. Therefore, it doesn't appear in your inbox anymore but is still accessible in the "all mail" folder or by using the search function within Gmail. This allows you to keep a tidy inbox without removing emails you may need at some point down the line.
The Delete option moves emails to the 'Trash' labels where they stay for 30 days before being permanently deleted.
To Archive in the Gmail mobile app just swipe left or right, if you archive something by mistake just hit undo in the dialog box that pops up for a few seconds.
To Archive in Chrome:
Check off all emails you want to archive and click the archive button.