I am having a bit of trouble understanding the point of the following relativity scenario.
Imagine two freely floating rockets (side by side) of height $L$ in outer space. The rockets have a light on top that gives a flash of light every second. A person who is attached to the floor of both rockets. They see the subsequent flashes one second after another too but a bit ($L/c$) later than the light that emits them. So the time at the top flows with the same rate as the time on the floor, according to both persons. Now one rocket starts to accelerate, parallel to the other, and at the same time, the lights on the top give a flash of light. The person on the floor of the accelerating rocket receives this flash of light a bit earlier than the person in the freely floating rocket. The rocket keeps accelerating and the lights give off the second flash of light. The person in the accelerating rocket receives this second flash not the same amount earlier as the first flash (otherwise the second person would receive the flashes one second after each other too), but a higher amount earlier as the first flash because the rocket is accelerating towards the second flash.
This means the person in the accelerating rocket sees that there is less than a second passed between receiving the two flashes. The same holds for all subsequent flashes. So for the person in the accelerated rocket time goes slower.
I understand that an accelerated ship would be the same as being in a gravitational field, therefore time would move slower for the accelerated ship. Therefore, I guess less time should pass between the two flashes of light, in respect to another observer.
However, I don't see the point of the scenario posing that the ship is accelerating towards light.
Does time slow down for the ship because it's moving towards light? Or just because it's being accelerated - therefore having the same properties as a gravitational field? What is the point of this scenario?
A layman explanation would be mostly appreciated.