From the Merriam-Webster Learner's Dictionary:
in order to
: to make it possible for something to happen
And according to Etymonline:
In order "in proper sequence or arrangement" is from c. 1400; out of
order "not in proper sequence or orderly arrangement" is from 1540s;
since 20c. principally mechanical, but not originally so ("and so
home, and there find my wife mightily out of order, and reproaching of
Mrs. Pierce and Knipp as wenches, and I know not what," - Pepys,
diary, Aug. 6, 1666).
Phrase in order to "for the purpose of" (1650s) preserves etymological
notion of "sequence.
It means sequence.
Your first question
I went there in order to meet her VS. I went there to meet her.
Could be any difference?
Yes. In order to is somewhat more formal.
Consider:
Little Johnny, why did you go to the store?
--I went to buy some candy.
--I went in order to buy some candy. (unlikely register)