The error has your answer: FK_CAT_CTGR_PRD_IDX_PRD_ID_CAT_PRD_ENTT_ENTT_ID
FK -> Foreign Key
CAT_CTGR_PRD_IDX -> Table Catalog_Category_Product_Index
PRD_ID -> Column Product_ID from the table above
CAT_PRD_ENTT -> Table Catalog_Product_Entity
ENTT_ID -> Column Entity_ID from the table above
So, your problem is that a foreign key from one of these tables to the other fails. Most likely, you have deleted a product and left something in the Catalog_Category_Product_Index. Run the following selects on your database:
SELECT * FROM catalog_category_product_index WHERE product_id NOT IN (SELECT entity_id FROM catalog_product_entity)
Delete those rows from your database and the index process should work.