In the stored program concept, both the instructions and the data (that the instructions operate on) are stored in the computer memory itself. Before the introduction of this idea, instructions and data were considered two totally different entities and were thus stored separately.
Thus instructions like data can be read from the memory and written to the memory by the processor.
The processor then addresses the memory, reads the corresponding instructions, executes them and according to the executed instruction, processes (reads and writes) data as well.
Computers that store both instructions and data on the same memory are said to be based on the Von Neumann architecture. Modern desktop computers are still based on the same stored program concept.
The basic idea of this concept is given in Figure 1: