Majorly is a loose, spoken way of saying “very” or “extremely.” I'm majorly tired means you are really tired, not that something is major in a careful, official sense. It is simply major plus -ly, and it still feels American, young, and a bit of its time — the kind of word you hear in chat, not in a school essay. Some older speakers find it a little teenage or even dated; younger speakers may barely notice it. Use it when you want the feeling of spoken English. Do not use it when you need to sound careful. (Some people also use majorly to mean “mainly,” but that is another use; here it is the “extremely” one.)