where does archive email go?

Into your "All Mail" folder.

If you want to actually delete mail from your Inbox, there is a switch in Settings where you can change the behavior between Delete and Archive. However, if you set your GMail account up as an Exchange account, this toggle does not exist on your device, you have to go to m.google.com/sync on your device to change this behavior.

iOS: Understanding Gmail Archive

http://support.apple.com/kb/HT4207

It should be similar behavior for all accounts with this option.

Yes, actually it does. With iOS, 'Mail' can archive Gmail messages on your iPhone, iPad, and iPod touch. Archiving messages allows you to store messages you're done with but don't want to delete. When you archive a Gmail message, it moves to the 'All Mail' folder. 'Mail' doesn't delete the message from your Gmail account.

dannylasvegas wrote:

Yes, actually it does. With iOS, 'Mail' can archive Gmail messages on your iPhone, iPad, and iPod touch. Archiving messages allows you to store messages you're done with but don't want to delete.

Yes, we know that and no one is disputing it.

dannylasvegas wrote:

When you archive a Gmail message, it moves to the 'All Mail' folder. 'Mail' doesn't delete the message from your Gmail account.

Well, that depends on your settings. You can set Mail up to Archive or Delete your Gmail ... I believe that the default is still to Archive, but you can change the behavior to Delete here:

Settings> Mail> Accounts> (Gmail account)> Account> Advanced> Move Discarded Messages Into> Deleted Mailbox (as opposed to the default "Archive Mailbox")