When a field of view is described as 120°, that refers to the total angle. So, 60° to the left of center and 60° to the right.
Most camera lenses show a very restricted subset of the field of view perceived by the human eye and vision system.
It is probably the case that the system is measured across the diagonal from corner-to-corner of a rectangle, because that's the longest and therefore most impressive-sounding number. But for this purpose it doesn't really matter if it's the diagonal or horizontal field of view — both are close enough.
To get a tactile feel of what this means: put both of your arms straight out in front of you. Now, widen them so each is about two-thirds of the way to straight out from your body — basically, they're the legs of a triangle with a 120° angle. This camera will approximately record anything in that cone.
I don't know what your experience of sight is and I won't presume, so forgive me if the following is obvious to you. If it is not, I hope it will be helpful.
Human vision is not primarily accomplished in the eyes — there is a huge amount of processing in the subconscious brain. This means that most people are only dimly aware of the concept of a field of view. Vision is only sharp in the very, very center, but the eye moves around and the brain builds up a mental model.
If I consciously just look forward, I have vague awareness of things off to my side. I've read that this extends to 170°, but because of this mental model I'm pretty convinced that I can perceive things directly sideways from me and even a little behind. This is my brain lying to me, but it's a generous lie because in most cases I move my head and eyes around enough to continuously refresh that area in my subconscious model.
Meanwhile, looking straight ahead, I have the general perception of about a 90° cone that I'm "looking at". Maybe a little less than that... somewhere between 60° and 90°. Even though the sharp part of my eye only covers about two degrees, I have the perception that this whole area is sharp and has my attention.
In photography, we call a lens that has a horizontal field of view of about 45° a "normal lens". That's because if I make a photograph with such a lens and print it at a standard size of around 10" (25cm) and then hold that print at arm's length, the perspective shown in the picture will more or less fit naturally into my direct view of the world.
If I took a picture with a lens that gives a 120° view and printed it the same size, it would appear to have distortion, because I'd be bringing things normally at the periphery into what, on the print, is my straight-ahead vision. So, even though the camera system you are looking at has a field of view narrower than the human vision system's peripheral view, it's definitely in the range that we'd consider "wide angle" in photography — in fact, "ultra wide angle".