Term for double meanings

Ambiguity:

• the characteristic of having more than one possible interpretation or meaning (AHD)

Amphibology:

• a sentence or phrase (as “nothing is good enough for you”) that can be interpreted in more than one way. (M-W)

• the use of ambiguous phrases or such as can be construed in two senses. A good example is Shakespeare's 'The duke yet lives that Henry shall depose' (Henry VI).( Chambers's Twentieth Century Dictionary)

Etymology:

• Gr. amfibolos ambiguous + logos speech.

• Double entendre: a word, phrase, etc, that can be interpreted in two ways, esp one having one meaning that is indelicate
• Pun: a play on words, sometimes on different senses of the same word and sometimes on the similar sense or sound of different words.
• Play of words: a pun or the act of punning

Ambiguous means that a phrase can have more than one meaning

http://dictionary.reference.com/browse/ambiguous

Does this help.