Ott means "there" and itt means "here"—and these parts reflect distance. "Itthon" is used where the home is close to the speaker and "otthon" is used to express distance like when the speaker is abroad or in a significant distance. (Even the next pub could be a significant distance so you don't have to over-think it ;) ) Sometimes even native speakers mix them up, but it is not frequent and is counted a misuse.
It depends of the distance of the adressed person, too. If I am home and you're at the next door, "itthon" is preferable. When you're in NYC and I am in Budapest in my home, "otthon" is more appropriate. When I am in your place and we talk about my daily routine I can say "Mit csinálok délután? Otthon vagyok." (What do I do in the afternoon? I am at home.) This is because both of us far from the home I referred to, even if you're at your home. If you're in my place (because my wife let you in) and you phone me where am I at 5pm, I can say "otthon vagyok" though you are close to the referred place and I am far from that. (Note that we express future with present tense, therefore this example is correct. A good thing that we have only two tenses in use, that may be a relief after all that fuss we do with aglutinating and all... :D :D :D )