Every online business owner must consider the issue of how to accept payments for whatever they are selling. Hopefully you will get paying customers, and they have to be able to pay you somehow. It is generally disputed that credit cards (or debit cards, which are basically the same thing in terms of accepting payments online) are the easiest and most efficient way to pay and get paid online.
Yet credit cards are not without problems. First of all, many people still do not have (or do not have anything in some cases!) Credit or debit cards. This also means they probably do not use payment processors like Paypal, which work mostly with credit cards (although they also work with bank accounts, and believe it or not lots of people do not have these either). This is why some sites online have instructions for sending checks or money orders through the mail. This is quite time consuming, and undercuts the convenience of shopping online. Still, it is an alternative to credit cards.
As an online merchant, you may be thinking that people without credit cards are not worth your trouble. After all, such people are most likely broke and will not order anything from you anyway, right? Well, not necessarily. Some people, especially older people, do not trust credit cards and do not have them for that reason. Others may have gone through bankruptcy. They may actually be in stable financial condition now, but because they ruined their credit a couple of years ago they do not have any credit cards right now.
A related issue is that of security. Many people, with some justification, have credit cards but do not feel secure giving their numbers online. They fear things like identity theft and hackers. While these things are not the norm, they do occur, so fears about this are not pure paranoia. Of course, their fear of using credit cards online as opposed to over the phone or even in person may not make much sense. Who is to say that the clerk in the retail store at which you shop is not a closet hacker who will steal your identity? The fact remains, however, that many people have a particular fear of divulging information over the internet.
All of these points to the need for alternative payment methods. Checks and money orders still work, but using snail mail options to order items over the internet is not really a match. People are more likely to just try to find what they need locally than take the trouble to send a check through the mail.
One method that is fairly new is accepting payments that are charged to the customer's phone bill. For this to work, the customer must have a mobile (or cell) phone. The companies who offer this service have gotten permission of the phone companies to make this system workable. It is also in some ways more secure than credit cards, as there is no need to give financial information over the internet.
Perhaps in the future new alternatives will emerge. Or credit card payments will become more secure, and hopefully people without credit cards will also have a way to do business online. The fact remains, however, that not everyone wants to use credit cards and this is a matter of personal choice that people should not be penalized for.