Context-free grammar is a formal grammar that describes a formal language and is used in the field of theoretical computer science and linguistics. It is a type of formal grammar defined by a set of production rules.

Definition of Context-Free Grammar:
A context-free grammar consists of a set of production rules that define how to rewrite strings of symbols. These symbols are divided into two types: non-terminal symbols and terminal symbols. Non-terminal symbols are placeholders that can be replaced by other symbols, while terminal symbols are the actual symbols that appear in the final strings.

Production Rules:
The production rules in a context-free grammar are of the form:
A → α
Where A is a non-terminal symbol and α is a string of symbols (terminal or non-terminal). This rule states that A can be rewritten as α.

Example:
Consider the following example of a context-free grammar:
S → aSb | ε
Here, S is a non-terminal symbol and a, b are terminal symbols. The production rules state that S can be rewritten as "aSb" or as the empty string (ε).

Context-Free vs Other Types of Grammars:
- Context-free grammars are more powerful than regular grammars (option B) because they can generate languages that regular grammars cannot.
- Context-sensitive grammars (option C) are more powerful than context-free grammars because their production rules can have context-dependent conditions. These conditions allow for more complex rewriting rules.
- English grammar (option A) is a specific set of rules used to describe the structure of the English language and is not directly related to the formalism of context-free grammars.

Therefore, the correct answer is option C - Context-sensitive grammars.