Hi,
I know absolutely nothing about electronics, but my son got a MK125 kit for xmas from a friend and I helped him put together. (Lord help us 
)
Anyway, on the diagram it shows a 12VDC power source, but also a battery with the the light bulb attached. Does that mean you need to have a direct power source and a battery source, or is that just to indicate that you should have either?
Sorry for wasting your time with such a basic query
“a battery with the the light bulb attached”
What’s that? 
Sorry, I don’t have this circuit so I can’t imagine that symbol.
But for your question: yes, of course, either a battery or a 12VDC can be applied to the circuit. In the jack, there’s also a switch that prevents the battery and the other power supply coming together, so it’s even safer to have only one power source, but it’s of course, unnecessary.
I mean, why would you need two power supplies? That’s unlogical; you only plug your computer once in the wall, not with two cables… 
But, never mind. 
So, does the circuit work?
Greetings, electron.
The circuit must be powered by a 12V DC adapter, the relais can control low- or highvoltage load’s.
The relais output is just a switch to control your specific load (mostly a lamp).