Why and how does complexity usually tend to increase through time?
This is actually a very interesting yet difficult question to give a single precise answer to. I will try and summarize for you a "meta answer":

Complexity Science Some consider complexity not to be a Biological topic as such, since it is a property that accumulates in non-biological systems e.g. economics, technology, music, language - in fact anything that "evolves" through time. This new field of science is called "Complexity Science" or "Complex Systems" and is primarily a field of mathematics or information theory: Complex systems

Complexity in Biology What I can say is that these kinds of questions have started an almost new field in Biology, called "diversity evolution", here is a very interesting paper: Diversity Evolution.

Defining Complexity You were right to mention Complexity first needs to be defined, and as an early field of science this is where much focus has been recently. There are quite a few definitions but it is perhaps too controversial to list any particulars... HERE is a whole UCL lecture dedicated to defining Complexity! 

Topics of Complexity Science I have written enough, so perhaps this lovely diagram of the topics of Complexity Science will be of some help: