I had issues understanding the use of "ground" when I was starting out as well. I managed to understand it a lot better when I worked this out...
As some others have pointed out you need to think of the Voltages (12V, 24V etc) as being based upon a reference, which is 0V.
Imagine you are standing on a flat surface, the floor. There are three ladders; red, green, and blue, leaning against a nearby wall. The red ladder has 24 rungs (24V), the green ladder has 24 rungs (24V), and the blue ladder has 12 rungs (12V).
However, the green ladder (24V) is not actually standing on the floor like the red ladder (24V). It is standing on a step which raises it 1 rung above the floor. This means that, while it is still 24 rungs (24V), it is potentially 1 rung higher when compared to the red ladder using the floor as the reference point.
Both the floor and the step are the starting points (0V) for their respective ladders so they each only go 24 rungs (24V) high. But, because the green ladder starting point (0V) is 1 rung (1V) higher than the red ladder, if you tried to step directly across from the top of one to the top of the other there would be a problem. If you step from the red ladder 24th rung (24V) to the green ladder you'd end up at the 23rd rung (23V). In the other direction, from the green ladder to the red ladder, you'd end up at a point where a 25th rung (25V) would be, but there isn't one, so you'd fall down 1 rung to the red ladder's 24th rung (24V).
The same issue occurs when you consider the blue ladder with 12 rungs (12V) and realise it is sitting on a step that is 2 rungs (2V) higher than the floor. If you step from the blue ladder 12th rung (12V) to the red ladder you'd end up on its 14th rung (14V)!
Grounding your system to the chassis is the equivalent of forcing every single ladder, whether it has the same number of rungs or not, to start on the floor. So, your ladders will all start at the same point (0V) and all the rungs count up from there.