Computer Architecture is essentially the principles and procedures that describe the capabilities, functions, programming model, and implementation of a computer system.
Computer Organization, on the other hand, is the interactive mix of hardware programs and users.
The study of Computer Architecture and Computer Organization aids in understanding the micro-level execution of computer instructions, hence facilitating the writing of programs that are faster, smaller, and less prone to mistake. It provides a sense of the relative cost of computer operation and the relationship between software and users based on their internal operations.