This change is called elision, which means the "e" is dropped and the apostrophe signifies its absence.
Here are some examples:
* ne + avoir: n'avoir (to not have)
* ne + elle: n'elle (not her)
* ne + heureux: n'heureux (not happy)
* ne + homme: n'homme (not man)
Important note:
This change only applies to the word "ne". Other words with a final "e" don't undergo elision. For example, "je" (I) remains the same even before a vowel.