Straight through processing (STP) is the processing of orders for dealing in securities purely through electronic systems with no paperwork involved and little human intervention.
This means that a fund manager can place an order on the systems run by a fund management company. This is then electronically passed on to a broker and execution takes place through an automated trading system with no manual intervention. Settlement then also takes place through automated systems.
Straight through processing is something that has yet to be achieved but the required technology and systems are under active development. STP is perfectly achievable. An important part of this are standards such as the FIX financial messaging standard that allow different systems to work together.