This option is available on Advanced Settings of Update Product feed only. When the published field is mapped, auto publish and hide will be disable. To enable it, please remove the Published field mapping. 
1. Auto publish products can be set:
Do not apply: No changes
All products in store: Auto publish all products in store if any one of the variants has a quantity of more than zero
Matching products within a feed file: Auto publish all matching products in the feed file if any one of the variants has a quantity of more than zero
It will auto publish all the products that the feed scans that the quantity is more than zero. If the supplier feeds updated 10 products with more than zero, it will publish those 10 products. 
2. Hide and archive products from all sales channels can be set:
Do not apply: No changes
All products in store: Auto-hide and archive all products from all sales channel when all variant is 0 and continue selling when out of stock are disabled.
Matching products within feed file: Auto-hide and archive all products from all sales channel that match with the products in the feed file when all variant is 0 and continue selling when out of stock are disabled.
It will auto hide all products that the feed scans that the quantity is zero. If the supplier feeds updated 10 products to zero, it will hide/archive 10 products. Continue selling when out of stock needs to be disabled.
Enable this option Only hide products from the online store and does not affect products from other sales channels