There is a somewhat mathematical description in twistor59's answer to What is the weight equation through general relativity?What is the weight equation through general relativity?. I don't think you're going to get any real idea of what is going on without some maths.
An alternative way of looking at the question is the river model - see my answer to If you shoot a light beam behind the event horizon of a black hole, what happens to the light?If you shoot a light beam behind the event horizon of a black hole, what happens to the light? for a discussion of this. In this model spacetime is flowing inwards towards the planet/black hole/whatever and freely falling observs are carried along with the flow just as you would be carried along by the water if you were floating in the river. Someone on Earth's surface is standing still against the flow, and there therefore feels a force just as (though the analogy is getting very loose here!) you feel the force of the water when standing still in a flowing river.
Be cautious about analogies like this though. Spacetime isn't a material like water and doesn't flow. It's the coordinate system that's flowing.