Gmail has "Archive" button for messages.
What exactly is the effect of "archiving"?
Is it the same as deleting?
Archiving in Gmail is simply the act of removing it from your "Inbox". By removing the "Inbox" label.
An archived email is not deleted. However, they are not immediately visible by default.
Archived email appears under "All Mail" (system label on the left hand side, under "Inbox"), but the "All Mail" system label is not displayed by default. Under Settings > Labels you can show/hide the "All Mail" label.
(As you can see from the screenshot, I should archive more!)
Reference (Gmail help):
Archive messages in Gmail