We give an overview of the operational concepts and architecture of the Kepler Science Processing Pipeline. Designed, developed, operated, and maintained by the Kepler Science Operations Center (SOC) at NASA Ames Research Center, the Science Processing Pipeline is a central element of the Kepler Ground Data System. The SOC consists of an office at Ames Research Center, software development and operations departments, and a data center which hosts the computers required to perform data analysis. The SOC's charter is to analyze stellar photometric data from the Kepler spacecraft and report results to the Kepler Science Office for further analysis. We describe how this is accomplished via the Kepler Science Processing Pipeline, including the hardware infrastructure, scientific algorithms, and operational procedures. We present the high-performance, parallel computing software modules of the pipeline that perform transit photometry, pixel-level calibration, systematic error correction, attitude determination, stellar target management, and instrument characterization. We show how data processing environments are divided to support operational processing and test needs. We explain the operational timelines for data processing and the data constructs that flow into the Kepler Science Processing Pipeline.