Don’t give away any damaging secrets. Don’t make public anything that should be kept private.
The proverb originated among children. To tell tales out of school was to sneak – to try to keep on good terms with the teacher by betraying other children. One of Mother Goose’s Nursery Rhymes runs:
Tell-tale-tit,
Your tongue shall be split,
And all the dogs in the town
Shall have a little bit.