Basically, Computer Architecture is the rules and methods which describe the functions, capabilities, programming model, and implementation of a computer system. 

On the other hand, Computer Organization is the interactive combination of hardware programs and users. 

The study of Computer Architecture and Computer Organization helps to know the execution of computer instruction at the micro level and its knowledge helps to write programs faster, smaller, and less prone to error. It gives an idea about the relative cost of computer operation, and the relationship between software and users by their inner working