Questions about ambiguity in context-free grammars.

A context-free grammar is ambiguous if some word has two different parse trees. Often this is undesired: for example, we would like $a + b \times c$ to be read as $a + (b \times c)$ rather than $(a+b) \times c$.

In parsing, ambiguity is removed through operator precedence and associative rules (does an operator associate to the left, like addition, or to the right, like powering).

Some classes of context-free grammars, for example the LL(1) grammars used in parsing.

Some languages are inherently ambiguous, that is, any context-free grammar for the language will be ambiguous. The standard example is $\{a^nb^nc^m\} \cup \{a^nb^mc^m\}$.