Time Machine - How does it work? I understand how Apple advertises Time Machine to work, but I want to know more in-depth.

Does it keep track of all file changes in a database or flat file that you make as you work so that it knows during the next backup process what to copy? It seems as when it does begin to backup, it happens so quick, so there must be some knowledge of file changes.
The first place to look for some in-depth Time Machine information is the late James Pond's web site: pondini.org. Details about how Time Machine is aware of file changes are in http://pondini.org/TM/Works.html.

It has not been updated since August 2013, but is still the best single source for Time Machine answers.