"a man who has nothing which he is willing to fight for [...]"
I understood it until nothing. What does which mean? Why is it there? Can I omit?
Yes, you can omit the "which".
My Grammar for English Language Teachers textbook has the following information, which might help you understand why the "which" can be omitted:
When can we leave out a relative pronoun?
We can choose whether or not to use a relative pronoun when the verb in the relative clause already has a subject. I and we are subjects of the relative clauses in the following sentences.
Main clause || Relative Clause
I tried to help a child || (that) I found in the street.
Paris is a city || (that) we always go back to.
One of the reasons why the "which" is included in your example is because it's less common for relative pronouns to be omitted in writing. It's more common that they are omitted in speech. In part, therefore, it's a matter of formality and style (noting that your example was written nearly 150 years ago!).