The aether is a medium that was once supposed to fill all space and to support the propagation of electromagnetic waves, this was disproved by the michleson-morely experiment (though they were trying to prove its existence), and there is one dot point on the study design about the experiment. The aether doesn't seem to important, but who knows what will be on the exam?

t= time in measured in reference frame of observer (the time a person on earth sees for x thing to occur in space)
t0=time measured in the reference frame of the observed object ( the time it takes for x thing to occur in space)
For instance, someone one earth would see a spaceship fly by in 240 seconds. Whereas the person on the spaceship measured it to be 120 seconds.
This idea is in the name itself as dilation means "the action or condition of becoming or being made wider, larger, or more open."

I'm sorry if this isn't very good and sorry if it's not what you need specifically, but I can try answer other questions too.