Overview
The titular character, Maxx, is a being who exist both in the "real" world and an alternate reality called the Outback. In the Outback, he is the the protector the Jungle Queen, but in the real world, he is a homeless man, who wears a purple superhero costume (see above). The Jungle Queen also has a "real world" counterpart named Julie Winters, who is a social worker that often bail Maxx out of prison. While Maxx is aware of both realities, Julie isn't.
Plot
In the first story arch, a serial killer Mr. Gone (who has a telepathic link to Julie) is constantly calling Julie, but she ignored him. The Maxx was protecting Julie, so Mr. Gone had to get help from the Isz, the main predators of the Outback. Mr. Gone reveal that he was once a friend of Julie's father; the Outback was actually controlled by her subconscious and other people have them; and Julie accidentally created a rip between the real world and the Outback causing the creation of Maxx. Julie started heal herself and her Outback. We meet a depressed teenager, Sarah, who doesn't want to be like her father, Mr. Gone.
In the second story arch, Julie and the former Maxx (whose name is revealed to be Dave) have disappeared, so this story arch focuses on Sarah. A giant yellow, slug monster called the Iago (who is from the Outback) came into the real world and has a list of people to kill... including Juile and Sarah. Sara (as she spells it now) was hounded by a homeless man named Norbert, who she realized is her "Maxx". Julie and Dave resurfaced to battled the Iago. Norbert, Sara, Dave, Mr. Gone and Mark (Julie's son) try to stop the Iago, who kidnapped Juile and went into Sara's Outback and save her. Mr. Gone reveal time is running out for the group. Then, they are reborn into a new reality. In this new reality, Mr. Gone is a professor and Dave is a janitor at the same school. It's implied despite living completely different lives, they still have connections to the Outback and each other.
References:
http://en.wikipedia.org/wiki/The_Maxx