Meaning of this sentence with would

My friend said I did not think I would marry her. Why did he use would in that sentence?

Your clause- I would marry her is sometimes referred to as Future in the Past.

We use it to express the idea that in the past you thought something would happen in the future. It does not matter if you are correct or not. Future in the past follows the same basic rules as the simple future. "Would" is used to volunteer or promise, and "was going to" is used to plan. Moreover, both forms can be used to make predictions about the future.

You can find more examples and information here: https://dictionary.cambridge.org/grammar/british-grammar/future/future-in-the-past