When we talk about density we are talking about how many grafts are placed in a square centimeter. You will often see it referenced as "X" per cm2 with "x" representing the actual number. Outside of the forums you will most likely refer to it as how thick your hair is or how thin.
There are so many factors that can affect density which could easily fill a book so of course I'll spare you. Understand though that different clinics have different views on what density is necessary for any given area of the scalp. The biggest debates usually revolve around densities of the hairline and what is appropriate when rebuilding them. Different clinics have different abilities and different views of what is necessary or even possible.
Various factors that affect density is hair shaft diameter, hair color vs. scalp color contrast, type of skin (can it handle incisions so close?), and of course trying to balance proper density in one area over another so that balance is maintained relative to age and overall donor supply.
This is definitely a micro summation of density but hopefully it doesn't confuse you more. Continue to read and ask questions and you'll do fine.
I am employed by Hasson & Wong, on salary, not commission. My opinions are my own. Beware of deceptive photo tactics used by clinics with both flash and studio lighting. Photo gallery patients are not models.