Here's another mental model, the balls model, which I sometimes find useful, especially in this case. Here it is in case it helps someone:

Imagine electricity as red balls, which can travel along conductors. Groups of red balls feel drawn strongly to places which have less balls, and away from places which have more balls, leading them to equalize quantities among all points in the circuit (let's assume for now cables can't store the red balls, only transport them. Points in the circuit are places that can store balls).

if you have a battery, both the sides can store balls, but assuming it's charged, the plus side might have 12 red balls and the minus side none.
The difference in red balls is 12! A quite strong force pushing red balls from the + to the -. (that's the voltage).
When the circuit is closed with a wire, the balls will travel quickly and end up with 6 at both the + and -. How many of them travel at once (Intensity) depends on how large the tube is (Resistance).

What if instead of 12 and 0 we have 112 at +, and a 100 balls at -? Well the force is the same as before (12), the whole circuit works the same way. 6 balls go from + to -, over the same amount of time (tubes have the same throughput), you then end up with 106 at both ends. You just have these 'residual' red balls hanging around, doing nothing special.

However, if you suddenly connect this circuit with 212 balls to the first circuit with 12, the balls will quickly flow from from the first to the second, this time with a force of a 200!
(The point here is that voltage is a relative measure, unlike charge.)

You might have an isolated electronic circuit starting with 12 and 0 balls, and think all is well. You touch the circuit once to start it, the balls are flowing normally. You leave it working for a few hours and come back, it still seems to be fine. You touch it, and ZAP, a spark, burnt smell, you're wondering what happened. Well the thing is that external sources can sometimes add a red ball or two to your system. Over time, they might add up, and after a while you end up with hundreds. As soon as you touch the circuit, they all flow to somewhere that has fewer.

Ok, where does the ground come into this? A 'ground' is like the - side of your battery. It's an object that can store balls the same way. However, instead of having one 'storage point' which can be filled with balls, it has a several. So take a metallic object, and say it has, for example, 11 storage 'points'. If you connect it to a single + point containing 12 electrons, the balls spread out so that there's the same amount of balls in each point (as we explained at the beginning). So after a while your 1 and 11 points, end up with one ball at each point. (Analog to the concept of capacity)

So the natural earth turns out to behave like a huge metallic object. So big that it basically has an infinite amount of storage 'points'. You can pour red balls into it all day, and still end up at an average of zero balls per point.

So now you take your 12 to 0 circuit and connect the - side to the earth. The difference between + and - is the same as before, 12. The flow from + to - is about the same (same resistance), so the circuit behaves almost the same. If however an external red ball is randomly added, it flows from the - to the earth, meaning that you never accumulate balls in the circuit.

This allows you to set a reference amount of 0 balls in every circuit you work with. Which is great. The amount of red balls at the + can still be set to whatever you like, and they will flow nicely from + to - along whatever circuit you create (like before), but on top of that you never run the risk of having red balls jump from one circuit to another if they accidentally touch, because there is never a large difference in red balls as they all have the same reference amount.

Anything big which is conductive enough can store a lot of red balls. So what qualifies? Soil usually works, water works to an extent (https://electronics.stackexchange.com/questions/164898/can-t...). When you can't connect to those a big object will have to do, like a car frame, it will have enough storage that over a short time it looks infinite, but if you really pushed and kept adding red balls at some point the reference level would change. With the earth you could pour red balls your entire life and barely make a difference to the reference level.

(So now you're thinking, the red balls are electrons, right? Well sort of, but don't tell a physicist! Otherwise they'll get angry and start talking about flow direction being this or the other way. Or they'll say something about non-rigorous representations, wave-particle equivalence, the balls actually being a 'lack of electrons' and we'll all be confused.)