When is a CFG ambiguous?
If we can find an $x \in L(G)$ such that for that particular $x$ we can have at least 2 different parse trees , then we can say that the grammar is ambiguous.
In compilers , in the syntax analysis phase , a parse tree is constructed by the parser with the use of LL(1) parsing table [Considering only LL(1) parsers here ]and is passed on to the semantic analysis phase.
How does this parsing takes place?
String is kept into the input buffer and each symbol is read from left to right and accordingly stack is either pushed with the RHS of a production or is popped.[Assuming here that you know how the process works].
Now where is the problem regarding ambiguity here?
Suppose i/p symbol is 'a' , and in a particular cell in the parsing table , say $Table[E][a]$ has two or more entries , this mean we've multiple choices here , using any might lead to an acceptance by the parser , but would lead to completely different parse trees , right?
Now can we say that grammar is ambiguous? No , we cannot always say that the grammar is Ambiguous. Why? By using a particular production , out of one possible production , might lead to acceptance , might not .
LL(1) parsers might get confused as to which production to be used in this case , and since LL(1) parsers are predictive parsers , it rejects grammar with multiple entries , so to reject the possibility of a possible backtracking while parsing .
