On my home page, no categories will display beneath the slider image. On your demo, the categories featured, space, tech and more articles are all displayed very nicely. I am finding it impossible to display anything.
When I investigate, my understanding is that I simply need to select the categories to be displayed in the Appearance: Leaf Options: Home Page Categories box. Problem is, it's blank.
When I try to solve the problem by creating categories in the "Posts" section, nothing shows up in the "Home Page Categories" box.
Not sure what else to do.