what this quotation meant by Frederika Bremer?

It means words can hurt people severely.

The point of a sword (pain) lasts a brief moment, but words that have a point (reason and value for having been said) can last a lifetime - those words can having lasting effects.

There is a saying "the pen is mightier than the sword". It means about the same thing as Bremer's statement. You can do a lot more (good or evil) with words - make greater changes - than you can by fighting with swords. ["Sword", here, is a metaphor, perhaps, for any kind of fighting or killing, no matter what the weapon. One can accomplish more with conversation than with war.]

It's pretty straightforward, but here you go:

Words can cut a heart in two more than a sharp sword.

And there are words that have the power to hurt you for the rest of your life.

This is a beautiful quote!! I HATED to break it down in such plain, un-beautiful words. :(

That sometimes the feelings that words cause (like a lover that says "I Don't love you" )hurt more than physical pain. It also means that while physical pain (like getting punched) hurts, the pain will go away. However, sometimes a broken heart may never heal.