How we cite our quotes: (Line)
Quote #1
Remember me when I am gone away,
Gone far away into the silent land; (1-2)
Well it seems like the memory can bridge huge distances, eh? Even though the speaker will be "far away" in the "silent land" of death, she will still be very close. By remembering her, the beloved will be able to keep the speaker "close."
Quote #2
Remember me when no more, day by day,
You tell me of our future that you plann'd: (5-6)
We see the same idea here as in lines 1-2. Even though the speaker and the beloved will no longer be able to communicate after she dies ("no more […] You tell me"), the beloved will remain in "contact" with the speaker as long as he keeps her in mind.
Quote #3
Only remember me; you understand
It will be late to counsel then or pray. (7-8)
The speaker's only real concern after she dies is that her beloved remember her. She's not afraid of the unknown, or worried about how her family will feel. Nope, not in the slightest. All she cares about is being remembered.
Quote #4
Better by far you should forget and smile
Than that you should remember and be sad. (13-14)
Okay, major contradiction alert here. Now the speaker would rather be forgotten? That seems to be the case. She realizes now that the memory, for all the good it can do, can also cause a lot of pain. She would rather her beloved not feel any pain on top of the pain of her death.