The word "house, home" (domus) is one of a few special words, plus the NAMES of cities, towns, small islands ( = only big enough for one city/town)--as distinct from the nouns "city, town, island"--that don't use the prepositions for directions (and location "in").
Accusative = motion towards (Like, "I'm going HOME" in English, vs. "I'm going to the office" or "to the store": so, HOME doesn't need the "to" or "towards" preposition in English either). So, Romam = to Rome.
Ablative = motion from. So, Roma (with long a) = from Rome.
"Locative" (the Romae / Bostoniae / Novi Eboraci that Duolingo teaches, for "I live in (place name of city)") is more complicated to describe. Here's what I tell my students:
all PLURAL place names: locative = same as ablative pl.
all 1st/2nd decl. SING place names: locative = same as gen. sing. (Novi Eboraci and Bostoniae are examples)
all 3rd decl. SING place names: locative = same as dat. sing. (or sometimes abl. sing.) . We don't have an example of one of these in Duolingo, so far as I've seen.
We could say that the ablative is usually used following a preposition; but that, in certain specific situations, the ablative is used alone (no preposition). City-names plus a few other words, including domus, don't need a preposition to express "motion away from," just the ablative ending. The instrument with which the subject does an action ("beats them with a stick") is expressed by the ablative ending alone. A point in time ("at midnight," "at dawn," "at the sixth hour," "in summer") is expressed by the ablative ending alone. And so forth.
Domum is the opposite of domo: domum is (TO) home/homewards, while domo is (AWAY) from home.
If I'm at the store, then I can go home: (Ego) domum eo.
If I'm at home, but am going to go to the store: (Ego) domo eo.
Eo ("I go") + either of 2 directions: homewards = domum; from home = domo.