Magento 1: What table links a simple product to a configurable product
The table catalog_product_super_link but the other tables that start with catalog_product_super_ are involved in the relation.
catalog_product_super_attribute - holds the configurable attributes
catalog_product_super_attribute_label - holds the store view labels for the configurable attributes - this is not that important
catalog_product_super_attribute_pricing - holds the price differences for the simple variations
There is also the table catalog_product_relation that seam to remember the configurable products relations.
After checking I confirm that the configurable products relations are remembered in 2 tables. This seams redundant but I'm sure there is a reason.
In the method Mage_Catalog_Model_Resource_Product_Type_Configurable::saveProducts() there is this that inserts the data in catalog_product_super_link :
And after that there is this that saves the data in catalog_product_relation: