TITLE: What does it mean to say a language is context-free?
QUESTION [21 upvotes]: What does it mean to say a language is context-free?

REPLY [17 votes]: Given the technical definition of what a language is and what context-free is, it means that in the processing of rules defining the language, no context is used. That is, any variable is rewritten by itself, with no context. Once a variable is produced in a derivation, none of the string around that variable will ever be involved in any further derivation...no context is used in rewriting a variable. 
More complicated languages do not have this restriction (they may allow use of context/other adjacent variables and terminals in rewriting a variable).
Context-free languages are "easier" to parse (quicker/more efficiently) than context sensitive ones.
Note that the term 'context' is very technical here; it is referring to the context of a substring when rewriting. Technical terms have a life of their own and don't necessarily relate well to the first layman's understanding of the word.