Position
Background position moves a background image anywhere on a page. It's not limited to a few specific location since you can get as granular as pixel values. When you are positioning, keep in mind that images start on the top left of the screen. Apparently, the positions are relative to the background-origin property rather than the page itself.
Attachment
Background attachment specifies whether a background image will scroll or not. I thought there would only be two values, but there's actually three options: scroll, fixed, and local. Scroll and fixed are the two you would expect, scrolling with the page and not scrolling respectively. Local means that it will scroll, but only as far as the assigned element's content.
Size
Background size sets the width and height of a background image whether indirectly with automatic values or directly with number values. The default auto value just uses the size of the image. Cover and contain both ignore something in order to do what they want. Cover ignores image values in order to cover the entire element, and contain ignores extra space in order to show the entire image.
Edge Offset Value
If you wanted to offset your image from the bottom left corner by 20px up and 10px right, there's a much easier way to do this than guessing with inaccurate pixel values alone or something like margin. Used along with positional words in the background-position property, each offset goes after each location. Therefore, the offset would look like this: bottom 20px left 10px.
Multiple Stack Order
By default, the color value actually goes first, then image, then the more modifier-like values. However, multiple images can be specified, and if they are, the color needs to be the last value after everything else. I saw something on Stack Overflow about the background color showing up under transparent pixels as a result of being placed last, but I still don't really get it. Whether there's one or multiple background images, there's still some image blocking out the color, so why would the first position work for one image but not multiple?
Summary
There are plenty of ways to make background images more interesting with some properties not even being mentioned here. You can choose to either specify all the properties separately or wrap everything in a single background property, but either way, I feel like loading images with CSS would be easier than styling HTML images.