The First Wave is a science fiction show about an alien invasion of earth in which the aliens (the Gua) can take human form. These tropes have been covered by others, however, what makes First Wave different is a focus on the psychological experiments (mind games) that the aliens perform on humans.
Cade Foster (the main character) is used by the Gua as subject 117, an experiment to see if certain personality types would pose greater resistance to their invasion than others. This experiment involves the aliens killing Cade's wife and framing Cade for the murder. Cade already has a police record, as he was a career criminal before he met his wife, and so he goes on the run.
Cade teams up with Crazy Eddie, a former physicist, who edits a journal called the Paranoid Times, and together they investigate cases of possible Gua activities. They are aided by a book of prophecies by Nostradamus which contain quatrains (riddles), which helps them to stay one step ahead of the Gua.
The Cade-Eddie relationship is key to balancing the tone of the show. Cade is very serious and earnest in his desire to defeat the Gua and Eddie is good at lightening the mood with comic touches.
During the first season, they meet a Gua called Joshua, who proves to be a prickly ally. Joshua is proud and loyal to his Gua heritage, but has doubts about the invasion and about the morality of attacking other worlds.
The first two seasons are largely composed of self-contained stories which do not contribute to a story arc. In general, the episodes contain a certain level of sexual content, in which the Gua exploit sexuality as a psychological weapon. Gua human husks sometimes sprout tentacles or emit the angry Gua voice. These bodies also disintegrate without a trace when Gua are killed, which makes proof of aliens challenging to acquire.
The third season is different from the first two. There are two new important characters: Mabus (leader of the alien invasion) and Jordan (leader of the resistance group called Raven Nation). Jordan becomes the first female character to appear in multiple episodes of the series. She gradually becomes Cade's love interest and is more developed as a character than the 'woman of the week' (human or Gua) in previous episodes. The show finds clever ways of using different actors to portray Mabus and keeping him both disturbing and mysterious.
I think it was clear that the show's creators knew that they weren't getting a third series. They used this an opportunity to complete their story over multiple episodes in which there is a connected story arc. The final confrontation between Cade and Mabus is appropriately a psychological one.
With hindsight, the show would have been stronger if the characters of Jordan and Mabus had been there together with multi-episodic stories right from the start in season one. However, I would still recommend watching this series for its treatment of psychological warfare.