Why the meaning of the sentence is "Das ist mein Ernst" I am serious?
It's just a fixed idiomatic expression. Literally, "Das ist mein Ernst" translates as "That is my seriousness". However, this literal translation doesn't make any sense in English and that's why you can't translate it word for word.
Another good idiomatic expression for this would be "Ich mein's ernst!" (literally "I mean it seriously") :)