The Query Optimizer is a critical component of database systems, responsible for improving the performance of SQL queries and DataFrame style APIs. It disconnects the "WHAT" from the "HOW" to compute desired results, translating user descriptions into an Initial Plan, which is then rewritten by the optimizer into an Optimized Plan that computes the same results but faster. Query Optimizers are implemented as a series of passes or rules that rewrite a query plan, composed of a sequence of these rules, and perform various types of optimizations such as expression simplification, predicate pushdown, and limit pushdown. These optimizers can improve performance in SQL queries and DataFrame style APIs, making them essential for industrial systems.