As Iceland is situated near the North Pole, it is possible to see the Northern Lights. Plan on visiting between September and March, when the nights are longest.
If you want to increase your chances of seeing the Northern Lights as much as possible, visit in March. The third week of March sees twice as many geomagnetic storms as usual, which means more lively and visible Lights.
However, keep in mind that seeing them is never a sure thing—it’s better to view it as a cherry on top of an already amazing adventure.