This checks for lands you control with the land type Plains or Island, not for lands named Plains or Island. The lands it checks for don't have to be basic lands. For example, if you control Watery Grave (a nonbasic land with the land types Island and Swamp), Glacial Fortress will enter the battlefield untapped.

As this is entering the battlefield, it checks for lands that are already on the battlefield. It won't see lands that are entering the battlefield at the same time (due to Warp World, for example).