If you enter an Arkham location that already contains a gate during the movement phase, you enter that gate and pass to the first location of the corresponding Other World during the Arkham Encounters phase; this constitutes a "normal" transition from Arkham to the Other World. Then, during the Other World Encounters phase of this same turn, you have an Other World encounter. Unless this Other World encounter specifically removes you from the Other World, you remain in the first area of the Other World location. On the next turn, during the movement phase, you pass from the first area of the Other World to the second area and resolve an encounter there during the Other World encounters phase. Again, if this encounter does not specifically eject you from the Other World, you remain there, and emerge from it (i.e. return to an Arkham location that contains a gate corresponding to your Other World location) during the movement phase of the following turn.
If, however, you are in a location in Arkham and a gate spawns on you, say, during the Mythos Phase, you are immediately drawn through the gate and delayed in the first area of the Other World. If you were not delayed, you would move from the first area of the Other World to the second area during the Movement Phase of the next turn, before having had an encounter there; thus, you would be able to emerge from the Other World and return to Arkham without having had two encounters in the Other World. This is why you are delayed when you are drawn through a gate that spawns on you; it guarantees that you remain in the first area of the Other World for the next turn and have an encounter there, as you normally would have to if you passed through the gate "normally."
Does that make sense? Hope so!