Often used in a humorous way; it means that someone has information from a secret source

“How do you know that this little package is a present for you?” “A little bird told me!”

“Come fai a sapere che questo pacchettino è un regalo per te?” “Me l'ha detto un uccellino!"

A version of this saying appears in John Heywood's 1546 proverb collection, another a few decades later in Brian Melbancke's Philotimus. The actual expression has been common since the 1800s