This sort of phrase is usually appended to a compliment of some
sort. It basically serves to nullify the complement and place the
other person in a bad light. If the person who you've complemented or
otherwise spoke positively of hears you append "She told me to say
that," you are often rewarded with a satisfying outraged expression,
especially if you say it with a smug grin on your face.
An example: "I don't have to
eat cat food anymore, because my girlfriend is such as good cook. She
told me to say that."
Do not overuse or otherwise abuse this phrase. Consequences can
include making the other person look like an ass for asking for a
complement, making you look like an ass for saying that the other
requested it, and possibly injuring trust between yourself and the
other person. It's a small disparaging remark that, when combined
with other small forms of seemingly harmless badness, makes
relationships taste like sour milk.