Okay kiddo, have you seen a piano before? You know how it has a lot of white and black keys that you can press to make music? Well, sometimes people want to play some special music that needs really low notes, like a big monster or a thunderstorm sound. But the regular piano only goes down to a certain low note.
So, what they do is change the piano a bit to make the lowest notes lower. Instead of having regular black keys like the rest of the piano, they make some of the black keys shorter and they put them in a different spot. This makes the lowest notes actually lower and helps people play very special music.
So, when someone talks about a "short octave", they are talking about this special way of changing the piano to make the lowest notes lower. It's kind of like giving the piano a superpower to make really deep, cool sounds.