In a product's SKU settings, you can elect to Keep Stock. Each sale of the specific SKU will reduce the in-stock count, down to zero. Once a product's SKU is at zero it will still display on the listing viewable by you members and the public, with a description box overlay that says 'Sorry, out of stock'. Once you add an available quantity to the SKU, the product will become available for purchase.
Sometimes you may want to show currently out-of-stock items so members know this will be available at some future date...however this may invite unwanted queries.
To remove a SKU from your public catalog, turn the SKU offline.
If a product is no longer available, turn the product offline.