The manager feature allows that a user locks away funds and grants the manager control over it. The user can only withdraw with a delay, which in turn means that the manager has enough time to react to it and adjust the balance if needed.
This can for example be used as a deposit into a CEX. Locking away funds on the BitShares Blockchain represents a deposit into the CEX, which allows the user to trade on the CEX, while the CEX does not need to be the custodian of the funds. The CEX settles the trades of the user onto the Blockchain every X amount of time and recognizes when the user wants to withdraw. With the built-in delay the CEX has enough time to settle the user balance on the blockchain according to internal trades.
Other use cases are possible too, like a promotion programm within the BitShares Blockchain (lock away asset X and gain Y% every Z time period), and of course a savings account (lock away asset X, can only be accessed after waiting 3 days, no manager required)