How potential difference is created across the terminal of battery

 will try to explain with some examples. There is never a potential difference when there is equilibrium.

You can think of it as a height difference. Think of positive potential as a high point and the negative one as a low point or ground. So there is a height difference. A thing at the high point is bound to come down.

Similarly, whenever there is charge imbalance, a potential difference is created. I tried to explain as well as I could but the question of exactly how it is created is kind of an abstract thing. It's like asking how the height difference is created between the two points.