Iirc, and I could be getting this wrong, but different crops take and return different nutrients to the soil. So rotating where they're planted can help prevent depletion of the soil, while you can still use all the land available each season.
Agronomists describe the benefits to yield in rotated crops as "The Rotation Effect". There are many benefits of rotation systems. The factors related to the increase are broadly due to alleviation of the negative factors of monoculture cropping systems. Specifically, improved nutrition; pest, pathogen, and weed stress reduction; and improved soil structure have been found in some cases to be correlated to beneficial rotation effects.
Other benefits include reduced production cost. Overall financial risks are more widely distributed over more diverse production of crops and/or livestock. Less reliance is placed on purchased inputs and over time crops can maintain production goals with fewer inputs. This in tandem with greater short and long term yields makes rotation a powerful tool for improving agricultural systems.
Eventually, yes, but it's primarily about what nutrients are in the soil. You can grow tomatoes after potatoes* but that doesn't add any of the nutrients potatoes need back into the soil.
I don't actually know the nutritional needs of either of those crops
I don't actually know the nutritional needs of either of those crops
Good pair to choose if you're just guessing though; both being nightshades, their nutrient requirements will be similar. I'm not sure if potatoes need extra calcium like tomatoes though, I would guess not as that's for the sake of the fruit