Designating a primary console also unlocks several other features, including Remote Play on Vita and the ability to purchase and pre-order content via the PlayStation App and have said content automatically download to your PS4. The FAQ also states that once you've chosen a primary PS4, "you can use up to 2 systems concurrently: the system activated as your 'primary' PS4 system, and one other system."
The FAQ also claims that, if a primary console is registered to an account with a PlayStation Plus subscription, there will be "numerous benefits" available to other users on that system, such as access to online multiplayer. The PlayStation Plus-holding account does not need to be logged in to utilize this feature.
The PS4 FAQ doesn't specify what other benefits for secondary users PlayStation Plus offers, or if the features mentioned will be enabled with the PS4's day one patch. Maybe Sony is saving that answer for FAQ Part 2: Electric Boogaloo.