Specifically, it was an attempt to explain combustion and other oxidation processes such as rust within the framework of four-element theory of fire/earth/air/water. Through the 18th century, phlogiston theory got extremely elaborate as it tried to explain better observations while keeping the original theoretic framework: I have a reproduction of the first (1772) edition of the Encyclopedia Britannica, which devotes 40 folio pages to explicating it. Within three years of this, Lavoisier showed that the constituent responsible for combustion is part of the air, not the combusting body, and Priestly that it was a new element (which we now call oxygen), together throwing the whole construct into a cocked hat, to be replaced by modern elemental theory. It's a textbook example of Thomas Kuhn's paradigm shift process per The Structure of Scientific Revolutions. It's fascinating stuff to read about, though -- the world described by phlogiston theory is a rather odd place. I have toyed betimes of writing a steampunk novel set in a world where the Britannica articles on chemistry are exactly correct.
As for the word itself, it was coined in 1702 by German chemist Georg Ernst Stahl in Late Latin, from Greek, the neuter form of phlogistos, inflammable/burnt up, from phlogizein to set on fire, from phlog-, phlox flame.
These days, the concept of phlogiston is usually regarded as a prime example of how science marches on.