To be ambiguous is to exist in a state of vagueness or uncertainty.
For instance, an ambiguous picture can be designed in such a way that there are two or possible images. An ambiguous statement is a statement that can be interpreted in more than one way, such as you might find in a joke. One of these is a question such as "How do you get down from an elephant?" The answer -- " You don't get down from an elephant, you get down from a duck." This bad joke is possible because it has different meanings depending on whether it is being used as a noun or a verb and the ambiguity in this is what makes the joke humorous.