The JavaScript RangeError: Maximum call stack size exceeded occurs when a function repeatedly calls itself without a stopping condition, leading to the program running out of space to keep track of these calls. This error is often due to excessive function calls, mishandled recursion lacking a base case, or out-of-range operations. An example is provided with a recursive function, myFunc(), that calls itself indefinitely, resulting in this error. To prevent this, adding a base case or reducing excessive function calls is advised, as shown in an updated example where the recursive calls cease upon meeting a condition. Tools like Rollbar can assist in managing and analyzing such errors, providing real-time tracking and aiding in smoother code deployment.