The Unified Inbox puts the mail from all of your accounts into a single list, so a morning catch-up is one pass through one inbox rather than a tour of four. Every account is included automatically, with nothing to set up.
Opening It
Tap the account picker at the top left of the mail list and choose Unified. The same picker takes you back into any single account whenever you want to focus on one. See How to Change Current Account?
The same idea extends past the inbox. Unified Folders combines each folder across your accounts, so you get one Sent, one Drafts, one Trash. See Unified Folders.
Telling Your Accounts Apart
Because the list mixes accounts together, each account carries its own color, which shows against its emails so you can see at a glance where each one came from. Set it under Settings | Accounts | [select the account] | Account Color, and see What are the Colors for the Accounts? for the details.
Choosing Where BlueMail Opens
If you would rather start in one particular account, that is a setting: Settings | Global Settings | Advanced Features | Default Account when Launching App. See How to Change my Default Account?
You can also fix which address new mail is sent from while you are in the Unified view, with Default From in Unified Inbox on the same screen. See Configuring a Default Account and 'Send From' Email.
