When you get towards Vik on the southern tip of the island, there's a black sand beach and at Reynisfjara, there are some amazing basalt columns. First off, don't go into the water at Reynifjara - they have dangerous sneaker waves:
Basalt is a volcanic rock. When the magma cools, the basalt contracts. If it contracts evenly on all sides, such as from water flow, it forms hexagons. The hexagons propagate all the way down to form the columns:
Roof of a cave nearby
There is also the jagged sharp basalt - must be a different type of cooling pattern. Wouldn't want a shard of this to fall on your head.
High dive off the columns: