Metalanguages provide rules for programming language syntax to help compilers check for errors. They describe a language's syntax using notations like BNF, EBNF, and railroad diagrams. BNF and EBNF use text symbols while railroad diagrams use graphical symbols to represent syntax rules for elements like data types, structures, and control structures. The document provides examples of EBNF and railroad diagram syntax rules for arrays, multidimensional arrays, and arrays of records. It includes activities to identify valid and invalid code snippets based on the described syntax rules.