A context switch is the operating system's act of saving the complete current state of a running process — its register values, program counter (which instruction it's currently on), and other CPU state — into that process's Process Control Block, then loading a DIFFERENT process's previously-saved state into the CPU so IT can resume executing exactly where it left off. This is the fundamental mechanism that allows a single CPU core to give the illusion of running many processes simultaneously, rapidly switching between them.

Context switching is what actually implements the state transitions covered in the Process Life Cycle lesson — every time the scheduler decides to move a different process into the Running state, a context switch is what physically makes that transition happen at the hardware level.

Context switching itself accomplishes zero useful work for either process involved — the time spent saving and restoring state is time the CPU isn't spending executing either process's actual instructions. This overhead is precisely why a Round Robin scheduler's time quantum (from the Scheduling Algorithms lesson) matters so much: an extremely short time quantum causes the CPU to spend a disproportionately large fraction of its time context switching rather than doing real work, while a properly-sized quantum keeps that overhead to a small, acceptable fraction of total time.

Beyond the direct time cost of saving/restoring registers, context switches also often cause cache and TLB (Translation Lookaside Buffer, from the Virtual Memory lesson) invalidation — the newly-scheduled process's data typically isn't already sitting in the CPU's fast cache, so its first several memory accesses after resuming will likely be slower cache misses, an indirect cost on top of the direct switching overhead itself.