If the box is around the day, does that mean it will or will not water on that day? Why are there different stations?

The different Stations refer to the two outlet connections. The theory is, and this worked REALLY well on the previous model, you could have (for instance), Station 1 water every 5 days for 10 minutes and Station 2 water ever other day for 20 minutes. These new models only allow one to have a different watering duration for each Station. (If you make use of the different Programs (A, B, C), you can still set up different periodicities by setting a different Station to 0 minutes in each Program, but it is far from intuitive.) We've always programmed them for every day/other day/3 days/etc., so I'm not real sure about the box around the specific day, but I think it does indicate the day selected for watering.

Jill, yes you are correct: the box around the day is to indicate that you are currently selecting that day for watering. As to your other question, there are multiple stations in case you want to be able to water more than one area without having to move or adjust your hose and sprinkler every time you need something watered.