In this video, the pipelining of ARM7 processor is explained, detailing its three-stage pipeline - fetch, decode, and execute. The parallel execution in ARM7 allows for faster program execution compared to non-pipelining. With pipelining, fewer machine cycles are required for execution as instructions overlap in different stages. However, challenges arise with branch instructions leading to discarding of pipeline data, causing a delay in processing but still faster than non-pipelined execution.