Very much like the drivers license you need to operate your real car.
It registers the existence of your ‘web vehicle’ with the proper authorities who own and maintain the structure of the world wide web. It also determins what your name is to the world – like a personalized plate on your web vehicle. Every so often accounts with the companies through whom you have registered ( like the DMV for your real drivers license ) must be renewed and paid.
Without registration you are not allowed to drive on the information super highway.
This is the shell of your website itself. Your hosting company controls how big your website is, what core features it has ( like email & databases ), and also acts as the place in which the files that create how your website looks to the outside world are located. Periodically you must renew and pay the companies that own the hosting account for your website – like paying rent on the building your business is located in, or where you live.
Some registration companies also offer hosting and likewise some hosting companies also offer registration. Generally the only reason to not have both with the same company is if one or the other provides a cheaper price or more features.
The design of your website is what everyone will see when they visit yourdomain.com. Some hosting companies offer pre-canned or template websites which you can purchase or use to create your own website. The best sites are designed by professional designers, who not only know what is appealing to the eye, but also what constitutes proper working code.
Some designers will purchase your hosting and registration for you and then charge you a (often inflated) monthly fee. Unless you have a hosting/registration agreement with your designer generally they will only be responsible for the creation and maintenance of your website content, graphics, and code itself – nothing more. Think of the designer as the architect that creates what your internet store will look like. In most cases you will only need to pay your designer when updates or changes are made to the site, although policies vary depending on who you hire.