The letter i has two common sounds in English: its name /aɪ/, as in ice, and a quick, clipped /ɪ/ sound. You can hear that quick sound in The dog will sit. and That box is too big. In both words the i is short and relaxed, nothing like its drawn-out name.
A short i word is simply a word whose i makes the quick, clipped /ɪ/ sound, like the middle of hiccup, not its name /aɪ/ as in ice. In sit and big, the i is short: The cat can sit on the mat. That box is too big for the shelf.
The sound, not the spelling, is what matters, and spelling is not always reliable. Just keep in mind that the same short i sound can turn up spelled in different ways in some words, so expect a few surprises rather than a rule. What defines a short i word is the /ɪ/ vowel itself. That is the real boundary with long i: in sit the i is the quick /ɪ/ sound, while in ice the i says its name, /aɪ/.