But What about Meiosis?

I thought you'd never ask!  Let me say in advance that this is as complicated as we will get in High School Biology.  If you can make it through this, you'll be OK. :)

Meiosis is how we get the sex cells.  The problem here is two fold: How do we get genetic diversity? and  How do we get cells with half the usual number of chromosomes.

The answer is meosis. It's a double cell division!  The first division includes the recombining of the parent's DNA (literally the chromosomes donated by the grandparents recombine with each other). That answers the first problem.  The second division happens without the usual doubling of the chromosomes.  This means that when the cells split apart, each of them have only a half load of DNA (and they are ready to combine with another sex cell to create offspring that have the correct number of chromosomes).  That is the answer to the second problem.

I am not going to go into all the details here, but each round of division has the same phases as mitosis (Interphase 1, Prophase 1....eventually Interphase 2, Prophase 2, Anaphase 2, etc.).

I would like to point out here that in humans, this gives you four sperm cells (if happening in a male), but only one egg cell (if happening in a female).  The reason is that the egg contains all the organelles.  You can't split the cell's organelles four ways and get a functioning egg.  Sperm, OTH, just need the DNA and a way to get it to the egg.