Max Quantity is a setting that exists on both the listing level and the integration level. Max Quantity dictates the maximum amount of quantity Listing Mirror will send for any given listing to the marketplace. Example, if you have a SKU with 10 QTY, and you have Max Quantity set to 5 on eBay, LM will only send 5 QTY to eBay, even though you have more than that.
Some channels, like eBay, have selling limits where you can only list so many items at any given time. You can use Max Quantity to lower the inventory per listing that you are selling, so you can create more listings, for instance.
Max Quantity can be found on the listing level on the Edit Listings page for each listing. Setting it here will apply to ONLY that listing.
Max Quantity can also be found at the integration level for each marketplace. Setting it here will apply to ALL listings that fall under that channel.