Private banking is basically the bank providing family office services. They generally give you one contact person, that makes your money annoyances non-annoyances. You need a loan for something, they just go sweet talk everyone involved to make the loan happen for you.

They also invite you to all the bank's private events, so you can schmooze with other high net worth people. Banks are always sponsoring fancy events everywhere, and private banking clients generally get free invites.