Hosting is a service that allows you to publish your websites on internet.
It´s providers business to offer you web space, databases, e-mail addresses, additional products and storage for exchanging data. These providers offer web server space for customers where you can upload websites via FTP or a web-interface.
Many providers offer even the domain registration and DNS entries. For a comprehensive website you may need database support (sql, MySQL, Oracle) and the ability to execute various scripts and scripting languages (like PHP, Java, ASP, Perl and others).
It´s a prerequisite for various applications like online shops and other CMS systems. Lots of service providers offer web-hosting as a service, it´s useful to know your special system requirements and to compare many offers.