Items in the inventory manager are pre-populated with items in the Ecommerce > Products listing.
Inventory manger needs to be enabled on a per-product basis. When enabled, you can set a warning level and when a warning reminder will be sent out (e.g. if warning level is 10, and warning reminder is 1, after the stock hits 10, a reminder email is sent out every time this product is sold). Current stock allows you to indicate the current stocking level.
When items become out of stock, "add to cart" buttons on the website are replaced with an "out of stock" icon until the stock level is adjusted to a value above 1.