How does crossing over lead to greater genetic variation between individuals within a population?

Crossing over shuffles alleles between chromosomes, resulting in greater variance in the subsequent meiotic chromosomal separation. (Which I mention in the next paragraph.) Say you have two homologous chromosomes, one from your father and one from your mother. Instead of you subsequently passing these chromosomes down as they are, crossing over will take some parts from the mothers chromosome and put them onto the father's chromosome, and vice versa for the exact same parts. So you now have a chromosome made  from parts of both your mother and father's chromosome, which means more variance than if you just passed down, say, you father's chromosome in its entirety.

Another mechanism in meiosis that produces variation is when the chromosomes are aligned on the metaphase plate and then pulled apart in order to divide the cell - homologous chromosomes are pulled one each to either end of the cell, and there's an equal chance of your paternal or maternal chromosome ending up at either end. This means that when you pass on a set of chromosomes to your offspring, it will be a random mix of your mother's and father's chromosomes.

I'm not sure about the final one, is that self-fertilization or fertilization as in pollination or sperm/egg?