Problem:

Question: What is the biological mechanism behind the variation within sexually reproducing species? Obviously, the children are combinations, to differing degrees, of their parents. But how does the variation originate in the parents to begin with?

I'm not referring to evolution or mutations rather I have in mind things like facial structure and personality in humans, or fur coloring in dogs. I just thought I vaguely remembered there was some kind of driver of variation... For example, does the parent produce a variety of germ cells that purposely differ from the parent's geneome?

I just think I'm missing something here.
(I'm familiar with DNA and genetics having taken a biology class in college and remembering much of it, I just can't seem to put my finger on

this point...)
Explain the biological mechanism.