Peterson's solution is a classical algorithm that uses shared variables to coordinate access to a critical section for two processes. Each process uses a flag variable to indicate whether it wants to enter the critical section, and a turn variable to designate which process can enter next. A process sets its own flag, then checks the other's flag and turn to determine when it can safely enter the critical section without violating mutual exclusion. While this ensures only one process is in the critical section at a time, it may not work correctly on modern computer architectures due to assumptions about atomic read-write operations. Overall it provides a good conceptual model for solving the mutual exclusion problem in a way that guarantees progress and bounds waiting time.