The useEffect hook in React plays a crucial role in synchronizing components with external systems by executing functions after rendering, with its dependency array serving as a pivotal element determining when these functions should rerun. The dependency array, if left empty, ensures the effect runs only once upon component mount, while specifying dependencies prompts reruns only if those dependencies change, preventing infinite rerender loops. Developers often encounter challenges with infinite loops, particularly when state variables within the effect are also dependencies, or when dealing with complex values like objects and functions, which React checks for referential equality. Solutions include careful management of dependencies, using useCallback to memoize functions, and structuring component logic to adhere to best practices while maintaining ESLint compliance. Through real-world case studies, the text illustrates how proper handling of the dependency array can lead to efficient, clean, and maintainable React code, highlighting its significance in state management and rendering behavior.