1. She said she was from Japan.
This is an example of reported speech. In reported speech, the tense of the original statement is moved back one stage ("backshifting"). So here, the original would have been:
2. "I am from Japan."
The "I am" is the simple present tense. To report it, we first change the person ("I am" → "she is"), and then "backshift" the verb to the simple past tense ("she is" → "she was").
This use of the past tense reflects not the content of the statement (her origin), but the time of speaking.
Does it make any more sense now?
All the best,