Eastbound means going towards the east, or made for traffic that goes that way. A train, a bus, a plane, or a car can be eastbound. A road can have an eastbound side: the lanes that lead east. You see this word a lot on signs, in stations, and in travel news — “the eastbound train”, “eastbound traffic is slow”. It is a bit official. In ordinary talk, people often just say going east. Bound here means “heading for”, as in bound for Taipei. It tells you the direction of travel, not where something lives or sits. A city in the east is eastern; a person from there may be an Easterner; a train heading that way is eastbound. You can be from the west and still sit on an eastbound bus.