Featured Image Setting

Please excuse the rudimentary question here, but could someone please explain the basic build idea behind the ‘Featured Image’ Admin function?

Ultimately Im wanting to include the “Set Featured Image” function in my theme, but am quite confused on how it relates to ‘featured post’, ‘post-thumbnail’ and ‘featured image’ (that shows up in the img gallery panel). Doesn’t have to be complicated. Just need to know where to begin understanding it so that I can build it into my theme.

Much appreciated!
R