Note
her means towards hereüber means over
The combination of both words describes a movement towards the speaker.
The opposite of her is hin meaning towards there
hinüber describes a movement away from the speaker.
A way to remember this is the movement of the swing. It goes forth (away) and back, forth and back = hin und her, hin und her...
Usages of herüber
Die Frau sieht herüber.
The woman looks at him. lit. The woman looks towards here
Die Frau sieht zu ihm herüber.
The woman looks at him.
Sie lächelt zu ihm herüber.
She smiles at him.
We are watching the story from the eyes of the little man. So the smile comes towards us: herüber
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