Context switching is a process in operating systems where the CPU stops running the current process, saves its state, and loads the state of another process to run it. This allows multiple processes to share the CPU by switching between them quickly. The steps include the CPU running a process, an interrupt or scheduler trigger causing a switch, saving the current process's state, loading the next process's state, and then running the next process. Variables like the CPU's current process and each process's state change during these steps. Understanding these steps helps clarify how multitasking works in computers.