Ronald gives a very good answer. I just wanted to add that inside XPath constraint on a page etc, where you don't have accses to variables you can use the token '[%CurrentUser%]' to reference the currently loged-in user.
You should set an XPath to make sure that a customer can only sees its own stock. I assume that users and customers are related somehow. It's not clear to me what the entity source is of the datagrid, but if it is Product then your XPath should be something like [Product.VoorraadLeverancier_Product/customer_stock_customer/customerID = $CurrentUser/ID]. It all depens a bit on the relation between Mendix users and customer.
It might be more efficient to create an extra reference between customer and products so you can simplify the retrieval of all products from a certain customer.
Thanks for the reactions, after configuring the security level too Production it was as easy as filling in [System.owner='[%CurrentUser%]'] for the Xpath constraint.