What is von Neumann's architecture?

It does not have much of a secret in it, it's not something complex, it's the basics of everything we do in any computational activity, and it was only formalized that this is how the computer should operate. It defines that:

• There is a data entry
• a drive that processes this data
• and causes a data output
• The processor can store data temporarily in a memory where pure instructions and data are left

The entrance and exit can count on several forms. As can be seen in the Wikipedia image:

I believe that it has become dominant because it was one of the first, it is simple intuitive, it makes a lot of sense and it caters well to all problems. Perhaps also because it does not define many details which would make it obsolete fast.

Other architectures may opt for a slightly different organization, for example separating instruction and data memory, can treat input and output as something different, can do control handling and calculations completely separately. >     

In short, the architecture is basically this:

In what is characterized in:

• Input and output systems;
• Main Memory; and
• CPU (Processor / Processor);

The main memory functions as a closet in which it holds information, both in its own memory and new arrivals from the input and output systems. The CPU is in charge of working (doing calculations) with all this information, being exchanging data with the main memory, and at the end if necessary showing them in the output systems.

I think it is the most used because it is a simple system, very functional and well defined. If I'm not mistaken, other areas of computing work with slightly different architectures, but it is a great reference.