What exactly is a half space

I was wondering what it was in it's most basic form, I just started multi-variable calc and a question asked: How would you describe this 3 D region? x>3
The back of the book said something about a half space, and I looked it up and got an idea but I'm not so sure I completely understand it.
Like in this case does the half space only cut the x-plane or all 3 planes?

Imagine all of space, and cut it in half - that's what they mean. Kind of like a ray is to a line, that's what a half-space is to all of 3-d space. It doesn't matter what direction it points in or where it starts, it's half of the full 3d space.