I am currently doing some research on entropy and I am trying to get my head around the concept.

One thing that I am getting right now is that entropy is just an application of probability and statistics right? So it's not a force like gravity, but simply a result of a mathematical rule that says that, because there are so many probabilities of a system being arranged in a way, then this system will move towards the state where it is the most "spread around". I am getting this right?

What then would be some physical manifestations of entropy? (I've seen the example of an ice cube or a cup of hot tea, but I don't quite see how these two relate to entropy. Could you guys tell me how these two are related to entropy?).

Thank you!