The entire amount of something, as in The baby ate all of his cereal. This usage is relatively new, the word of being included only from about 1800 on.
No less than, at least, as in Although she looked much younger, she was all of seventy. [First half of 1800s]
Examples from the Web for all of
There was one instant of confusion in the faces of all-of absolute silence.The Lane That Had No Turning, Complete|Gilbert Parker