I always found it hard to explain to the lay person how the gravity they are feeling is caused by curved spacetime. Their reaction was just one of bafflement and they ended up thinking that it is just too advanced to really understand.
There is an excellent answer to how curved space time causes gravity here: How does "curved space" explain gravitational attraction?, but that level of explanation is exactly of the mathy kind that would make the layman's eyes glaze over.
A few years ago I came up with an analogy which made intuitive sense to me and people were starting to "get" when I explained it to them. I don't have a deep background in the math of general relativity and have mostly just repeated other peoples analogies when talking about it, so I can't judge if this analogy is correct.
If you're in a car traveling at a constant speed and the car enters a turn, you are pressed against the side of the car. If you're in a rollercoaster and the track curves upwards you experience being pressed into your chair. (This is a familiar experience for most people and they accept it)
You are currently sitting in a chair, at rest. But now imagine that you are not actually at rest, but rushing into the future with one second per second. You are not at rest. You are moving in time. It is space-time that is curved according to the model in general relativity. The mass of the earth causes the rollercoaster track you are traveling forward in time on to be curved "upwards". Thus, when you sit at rest in your chain rushing into the future you experience being pressed into your chair.
This makes intuitive sense to me and the non-physics people I have tried the explanation on, but is it correct?