I have read this sentence in a story: "He had to see her for himself."
I would like to know what difference does "for" make in this sentence. If I omit it, would the meaning of the sentence be exactly the same?
"See for yourself" is an idiomatic way of saying that you want to see something first-hand, usually following the reports of other people.
For example:
If you omit the word "for" in your example, the overall intention (ie 'seeing' it) is pretty much the same, but it doesn't carry the same idiomatic meaning of proving something to yourself.
See something for yourself has a particular meaning; to convince yourself that it is real by seeing it with your own eyes. Without for, the sentence doesn't necessarily carry this meaning.