Who's The Giant Blue Guy?

That would be Dr. Manhattan. Yes, he spends a lot of the film naked; being transformed from an everyday nuclear scientist into what is essentially a glowing blue god with powers and perspective beyond those of normal human beings tends to make you less bothered about things like "clothing," apparently.

Manhattan - formerly Jon Osterman - is the only member of the Watchmen cast with superpowers; all of the others are, in their ways, mostly regular people in ridiculous outfits who fight crime with the help of technology and training... Batman, to all intents and purposes. Nite Owl is the most direct Batman-analog (complete with Batmobile-analog, the Owlship... although you can blame that one on Nite Owl's more direct inspiration the Blue Beetle), but both Rorschach and Ozymandias split well-known Batman traits between them (Rorschach gets the detective skills and obsessiveness, while Ozymandias is given the intelligence and faultless strategic-planning, as well as an element of the Bruce Wayne lifestyle); in comparison, Silk Spectre and the Comedian are more generic character types (Spectre in particular; Watchmen is a curiously male story) that owe less to superhero history and more to general popular culture archetypes.

That Manhattan becomes more than human is an important part of Watchmen; in plot terms, it alters the balance of power politically, allowing for America to become the particular dystopia that it is by the time the story takes place, but it also allowed Moore and Gibbons to step outside of the story to an extent and explore less immediate themes and more inventive storytelling techniques through the character's eyes. Manhattan's inhuman perspective also acts as an important counterpoint to the all-too-human failings of the other characters which drive the story. In many ways (and, perhaps ironically considering the emotional detachment of the character), Manhattan is the heart of Watchmen.