Here, “assigned” means the gender that people (Mom, Dad, doctors) decide that a baby is when he/she is born, based on anatomy. The idea is that the gender “assigned” by others based on anatomy may be different from the gender that the person feels he/she is. This word “assigned” has recently come into common use in the U.S. to make the distinction between the conventional designation of gender based on anatomy and the personal experience of gender identity (which sometimes does not match anatomy).

you can think of it as something given to you by god.