A context-free grammar consists of a number of productions. Each production has an abstract symbol called a non-terminal as its left-hand side, and a sequence of one or more non-terminal and terminal symbols as its right-hand side. For each grammar, the terminal symbols are drawn from a specified alphabet.
Starting from a sentence consisting of a single distinguished non-terminal, called the goal symbol, a given context-free grammar specifies a language, namely, the set of possible sequences of terminal symbols that can result from repeatedly replacing any non-terminal in the sequence with a right-hand side of a production for which the non-terminal is the left-hand side.
Context-free grammars are named as such because any of the production rules in the grammar can be applied regardless of context—it does not depend on any other symbols that may or may not be around a given symbol that is having a rule applied to it.