Vector processing involves executing multiple operations simultaneously by utilizing vectorized computer code, which allows for parallel processing of operands through pipelined math processors. The efficiency of these operations is contingent on the width of the data bus and the number of available math processors, enabling rapid computation as operands are read from memory. This approach facilitates complex calculations, such as matrix multiplication, by allowing additional operations like summation to occur without storing intermediate results. Scoreboarding is a technique used to manage the outputs from these vector operations, with historical implementations seen in the CDC 6000 series from 1964. Overall, vector processing significantly accelerates computer code execution by optimizing parallelism and resource utilization.