This checks for lands you control with the land type Swamp or Mountain, not for lands named Swamp or Mountain. The lands it checks for don't have to be basic lands. For example, if you control Stomping Ground (a nonbasic land with the land types Mountain and Forest), Dragonskull Summit will enter untapped.

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