‘All of a sudden’ means suddenly.

‘All of a sudden’ sounds like the kind of poetic version of ‘suddenly’ that would do justice to Shakespeare. In fact, that’s what Shakespeare thought too, as he used the expression in The Taming of the Shrew, circa 1596:

Is it possible That love should of a sodaine take such hold?

[Note: ‘sodaine’ was one of the numerous Tudor spellings of ‘sudden’.]