We say that a grammar is ambiguous if there is a word for which there is more than one parse tree. This is usually a bad thing because it entails that there is more than one way to interpret a word (i.e. it leads to semantical ambiguity).
As an example consider the following alternative grammar for arithmetical expressions: We define where is given by:
Each parse tree correspond to a different way to read the expression, i.e. the first one corresponds to and the second one to . Depending on which one is chosen an expression like may evaluate to or to . Informally, we agree that binds more than and hence the 2nd reading is the intended one.
This is actually achieved by the first grammar which only allows the 2nd reading: