A temperamental outburst; a tantrum.
The allusion in this expression may be to the hissing and spluttering of such an outburst, or it may simply be a contraction of 'hysterical'. The term originated in the USA in the mid 20th century and is first recorded in a 1934 edition of American Speech:
"Hissy is probably provincial slang. I have heard it for eight or ten years. He threw a hissy or He had a hissy means that a person in question was very disturbed and very angry."
'Hissy fit' was little used outside of the USA until the late 20th century. More recently, it has gained currency elsewhere, primarily due to its use in the media when describing the antics of various high-profile celebrity divas; for example, in September 2004, The Daily Mirror reported Sir Elton John's arrival at Taipei airport:
"Sir Elton, who arrived by private jet for the final concert of a Far East tour, clenched his teeth in fury when he saw a crowd waiting for him at the airport. Exploding in an extraordinary hissy fit, the 57-year-old star raved: "You're all rude, vile pigs!"
See other phrases that were coined in the USA.