Auto-Update
By choosing this option, the eBay Listing module will update your eBay listing every time you update one of your Miva product's Name, Price and/or Description.

Since eBay does not allow an Item's Name (Title), Price and Description to be changed once listed, the actual update is achieved by initially removing your item from eBay, and then re-listing it again.

Auto-Remove
By setting the 'Auto-Remove' option, the eBay Listing module will attempt to remove your product from eBay when you delete it from your Miva Store Product list.

See this document for information about Removing a product from eBay.