The agent is the official record keeper. It knows every registered holder, handles direct-registration accounts, runs the drip plan if there is one, distributes proxy materials, and executes the mechanics of a stock-split, a spin-off, or a rights-issue.
For most investors the agent is invisible because the broker sits in the way, but it becomes visible in three situations: holding through DRS, receiving shares from a corporate action in a company you do not hold at a broker, and chasing an unpaid dividend.
Example: a 2-for-1 split is processed by the agent. It updates the register to double each registered holding and instructs dtcc to double the depository position, which brokers then allocate to their clients overnight.
Related: direct-registration, street-name, dtcc, corporate-action, drip