You need to host your site because if you don't know one will be able to see it. The way you host your site is dependant on what you want to do with it. You will often get free hosting with the company who supplies your Internet connection, however this kind of hosting often has restrictions both in how much you can put on it and technically what it is capable of.
If your website is for business purposes you may wish to look to a third party to host your site as this gives you much more flexibility in terms of price, reliability and capability. At Duo we try and host all the sites we design. We bulk buy hosting to keep prices low and because we have full control of our hosting we can make sure it is capable of doing what we need. As our own sites are ran from the same hosting we also make sure the servers stays reliable.