Whether you're buying in a store or buying online, everything you do is geared around a transaction: the basic exchange of money for goods or services. In a real-world store, you simply take your new jeans to the checkout, hand over some cash, and leave the store with your purchase in a bag—that's a transaction. It works in a similar way if you're buying online, but there's one important difference: you never actually get to handle (or even see) the goods until they arrive at your home sometime later.
If this makes buying online slightly problematic for the purchaser, it also introduces two extra problems for the retailer (or e-tailer, as online retailers are sometimes known). Apart from having some means of processing transactions online, it means they also need a way of checking that the goods you've ordered are actually in stock and a means of dispatching and delivering the goods to your address.
In short, then, e-commerce is about combining three different systems: a web server that can manage an online storefront and process transactions (making appropriate links to bank computers to check out people's credit card details), a database system that can keep a check of the items the store has in stock (constantly updating as people make orders and ideally making new orders with suppliers when supplies run low), and a dispatch system linked to a warehouse where the goods can be instantly located and sent to the buyer as quickly as possible.
Only the first of these three systems is strictly necessary for e-commerce. Many people successfully run small-scale online stores without complicated databases or dispatch systems: they simply have a website to publicize their business and take orders and then manage the stock control and dispatch in more traditional ways. Small traders who sell items on the auction website eBay often work in this way, for example. Their "databases" are in their head; their "dispatch system" is simply a walk to the local post office.