The 8086 microprocessor architecture utilizes parallel processing with a Bus Interface Unit (BIU) and an Execution Unit (EU) that work simultaneously to enhance performance. The BIU manages connections to external devices, carries out bus operations, and employs an instruction queue for efficient instruction fetching, while the EU is responsible for decoding and executing instructions using dedicated registers and an Arithmetic Logic Unit (ALU). The software model of the 8086 helps programmers understand functionality without needing detailed hardware knowledge, emphasizing the importance of registers and memory organization.