Safekeeping occurs when a broker-dealer holds securities that are registered in a client's name for the client.
The advantage from the client's perspective is that the securities are safe and the broker-dealer has them available to sell at the client's instruction.
The disadvantage from the broker-dealer's perspective is that securities held in a client's name are not fully negotiable or fungible, so they can't be used to settle trades, for example. Thus, it's a service for which many firms charge a fee.
Instead of being registered in their own names, clients' securities may be registered in the broker-dealer's name or in the name of a depository. That's known as being registered in street name or nominee name.
With this type of registration, the client's ownership rights are fully protected but the stock is fungible. The broker-dealer may use a limited portion of the holding to settle trades or for other purposes.