Omni-channel means establishing a presence on several channels and platforms (i.e. brick-and-mortar, mobile, online, catalog etc) and enabling customers to transact, interact, and engage across these channels simultaneously or even interchangeably.
Giving the customer the convenience and flexibility to purchase an item using your shopping app, and then letting them pick up the merchandise in your store, plus allowing them to process a return via your website, is an example of omni-channel retailing.
It’s important to note that omni-channel goes beyond simply being on multiple channels or platforms. Just because you have a website, a mobile app, and a physical store doesn’t necessarily mean that you’re an omni-channel retailer. In order to truly be one, you must fuse all those channels together so they give customers a seamless experience.