Hosting the web site yourself means that you will need to have the right equipment, including a web server and a permanent connection to the Internet. You would need to ensure that your Internet service provider (ISP) allows this type of usage too. You would also need to have web site administration skills such as managing/configuring a web server, patch management, firewalls, virus protection etc
Most people don't do their own web site hosting. Even if they have the skills or equipment, it often makes more sense to hand this task to a third party who can monitor the web site 24/7.