Literal Definition: Serious and a Half
Basically, Seriously.5 is an enhancement to a dialogue that is said when the audience is in disbelief at the authenticity of an argument, event that took place etc... The speaker then re-establishes the argument as being Serious.5 which would therefore add extra emphasis to how "real" or "true" the speaker's statement actually is.
Steve: "Yo man, did you hear about Maria hooking up with Julian at that party?"
Dave: "GTFO brother, I was planning on going for that!" (reluctant to believe the story)
Steve: "Trust me, they were smashed out of their minds and I was right there when it happened bud; I'm being completely Seriously.5 right now."