Think about visiting a fast-food restaurant. When you order a burger, person behind counter might ask if you want fries with that. That is cross-selling. Then, they might ask if you want to make your drink super-sized for just a few cents more. That is up-selling. Both techniques help businesses sell more, but they work in slightly different ways.
Cross-selling means inviting a customer to buy extra items that complement what they are already purchasing. If you put a digital camera into your shopping cart, online store might show you a list of matching camera bags, memory cards, or batteries. You did not originally plan to buy these extras, but because they match your main purchase perfectly, you add them to your order. It makes shopping convenient because you get everything you need in one place.
Up-selling means convincing a customer to buy a more expensive version of item they are looking at. If you are browsing for a standard laptop, store might show you a banner comparing it to a luxury model that has a faster processor, bigger screen, and longer battery life. Goal is to show you that spending a little more money right now will give you a much better experience in long run.
Online stores use automated recommendation systems to display these offers at perfect moments, like on product pages or right before checkout. When done correctly, it does not feel pushy. It feels like helpful advice that improves customer satisfaction while increasing average order value for store.