What does the phrase "Fee-fi-fo-fum" actually mean?

Fee-fi-fo-fum;

I smell the blood of an Englishman.

Be he alive or be he dead,

I'll grind his bones to make my bread.

^{Joseph Jacobs, Jack and the Beanstalk (1890)}

I've read about the origin of 'Fee-fi-fo-fum' but what does it actually mean?

It's a nonsense phrase, developed by the writer of the old English fairytale "Jack and the Beanstalk". It is usually expressed as fee-fi-fo-fum and it has no meaning or relevance besides the fact that it makes a neat couplet designed to strike terror into the listener's heart. As a child hearing this story, I always imagined the giant stomping his feet to the beat of fee-fi-fo-fum and making the ground shake and poor Jack's knees tremble.

Wikipedia covers the meaning well and has this to say about Jack the Giant Killer:

Neither Jack or his tale are referenced in English literature prior to the eighteenth century, and his story did not appear in print until 1711. It is probable an enterprising publisher assembled a number of anecdotes about giants to form the 1711 tale.

The article mentions that in William Shakespeare’s play, King Lear (written between 1603 and 1606), Edgar exclaims:

Fie, foh, and fum,
I smell the blood of a British man.

The article goes on to explain:

The verse in King Lear makes use of the archaic word "fie", used to express disapproval. This word is used repeatedly in Shakespeare's works, King Lear himself shouting, "Fie, fie, fie! pah, pah!" and the character of Mark Antony (in Antony and Cleopatra) simply exclaiming "O fie, fie, fie!" The word "fum" has sometimes been interpreted as "fume". Formations such as "fo" and "foh" are perhaps related to the expression "pooh!", which is used by one the giants in Jack the Giant-Killer; such conjectures largely indicate that the phrase is of imitative origin, rooted in the sounds of flustering and anger.

However, King Lear isn't the first work in which the phrase appears. English dramatist Thomas Nashe in 1596 wrote in Have With You to Saffron-Walden the passage:

O, tis a precious apothegmaticall Pedant, who will finde
matter inough to dilate a whole daye of the first
inuention of Fy, fa, fum, I smell the bloud of an
Englishman …

So it seems that writers have puzzled over the origins of this chant and what it means for over four centuries!