The mathematics of how irreversibility emerges statistically will require it’s own discussion, but for now let’s attempt to visualize some familiar physical processes that display irreversibility. The simplest possible case is dropping something, like a rock. When held in the air the rock has concentrated gravitational potential energy that turn into kinetic energy as it drops. Say you only drop it a few feet, not enough to break the rock. But do you hear it hit the ground? If you do then that means the collision caused a lot of local wiggling of the air molecules and it gave off a little bit of heat, and this energy has been dispersed in such a way that it can never be recovered. In an idealized limit, you can call such a process reversible if you imagine performing it infinitely slowly, such that at no point in its trajectory does the rock cause even the slightest disturbance of the air around it. The point to take from that example is that the reversible case is an idealization. Its also a good one in this case because the entropy produced by the collission is small enough to be negligible. But if the rock is dropped at any real speed, there will be some random mixing of the environment around it, and thus some irreversible component to the process. A clearer example is to imagine a liquid being poured onto a flat surface. It is dissipating gravitational potential energy as it falls, which causes it to stay together, but once it’s on the flat surface the gravitational potential is the same in every direction the liquid can move. What does it do? It spreads out, obviously.