Grammar formalisms are structured systems used to describe the rules and principles governing the syntax and structure of languages. They provide a framework for understanding how words and phrases combine to create meaningful sentences. Common examples include context-free grammars and regular grammars, which help linguists and computer scientists analyze language patterns. These formalisms are essential in fields like computational linguistics and natural language processing, where they enable the development of algorithms for language understanding and generation. By formalizing language rules, grammar formalisms facilitate the creation of tools such as parsers and compilers that process human languages and programming languages effectively.