Wikipedia has an incomplete entry for it here and a much better one in Spanish here. Basically it’s just two rocks — one large flat rock at the base and a smaller, rounder (or oval) rock which is used to crush or grind the ingredient between the two. It’s like a large version of a mortar and pestle.
One would think that a food processor could easily replace it, but according to my grandma, the taste and texture of the result is completely different.
The batán is used to grind all kinds of ingredients. It’s used to crush corn and cilantro for green tamales, and huacatay combined with aji amarillo for aji de huacatay. If you gave my grandma the choice of using an electric coffee grinder, or the batán, she’d grind her beans with the batán every time.
Photographs by Michael Findley