The unified inbox shows mail from all your accounts in one place. The folders at the top of the desktop sidebar, and at the top of the menu on your phone, combine every account: Inbox, Unread, Starred, Sent and the rest. On a phone it's simply called Inbox.
To see one account on its own, open it under All Accounts in the desktop sidebar, or under Accounts in the phone menu. On desktop, ⌘1 to ⌘9 (Ctrl+1 to Ctrl+9 on Windows and Linux) open each account's Inbox, and ⌘0 (Ctrl+0) brings you back to the unified inbox.
Steps
To leave an account out of the unified inbox:
Desktop
Open Settings: press ⌘, on Mac, or Ctrl+, on Windows and Linux.
Go to the Accounts tab and select the account.
Under Unified Inbox, switch off Show in Unified Inbox.
iPhone, iPad & Android
Open the menu and tap the Settings gear at the bottom.
Tap Accounts, then the account.
Switch off Show in Unified Inbox.
Switch it back on the same way. The setting is saved to your Newton account, so it applies on all your devices.
Good to know
A hidden account keeps working. Its own folders, search and notifications don't change; its mail just stays out of the combined folders and the unread badge.
The unified Inbox names any hidden accounts at the bottom of the list. Click or tap Manage there to change the setting.
The unified folders appear only while at least two accounts are included. With one account, its folders sit at the top instead, and the switch isn't shown.
Labels and folders you create, and Gmail's Promotions and Social, appear only under their own account, not in the unified folders.