Questions & Answers about ההצלחה שלה במבחן חשובה לה מאוד, כי היא למדה כל השבוע.
In Hebrew, present-tense sentences like this often do not use a separate verb meaning to be.
So:
ההצלחה שלה במבחן חשובה לה מאוד
literally works like:
Her success in the test very important to her.
That is normal Hebrew.
If you wanted past or future, then Hebrew would usually use a form of היה:
- ההצלחה שלה הייתה חשובה לה = Her success was important to her
- ההצלחה שלה תהיה חשובה לה = Her success will be important to her
ההצלחה שלה means her success in a specific, definite sense.
The ה at the beginning makes הצלחה definite: the success.
So ההצלחה שלה is basically her success / the success she had.
If you said הצלחה שלה, that would sound more like:
- a success of hers
- one success she had
So the version in the sentence points to a particular success, not just any success.