The average website is a collection of files, including text and images, more or less the same as the files you find on your computer. For a website to be online, these files need to be stored, or hosted, on a server which is connected to the internet, 24:7. This type of storage is called web hosting. Unless you're wealthy and fancy buying your own server, you need to pay a specialist company to 'host' your website on their servers. It's that simple.
The vast majority of websites that are found on the internet are hosted on what's called 'shared hosting', which means they are stored on a server which they share with hundreds or maybe thousands of other websites. Shared hosting is inexpensive, costing as little as $4-5 a month. Obviously, not all web hosting companies are equal. Cheaper hosting companies generally cram the maximum number of websites on each server, which ultimately affects performance. It's not 100% true, but as a general rule, you get what you pay for.
Assuming you're thinking of ordering your first website and aren't expecting thousands of visitors a day, shared hosting is almost certainly all you need. If your site starts to get busier, you can always upgrade your hosting to deal with the higher traffic levels. The important thing is to find reliable hosting. Rather than read the forest of fake reviews that infest the internet, try searching user reviews on sites such as webhostingtalk.com for feedback on hosting providers.
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Wordpress is a program which creates and runs your website for you. Thanks to the multitude of free and paid-for add-ons, Wordpress is a superb choice for websites which need sophisticated functions and facilities, or if you want to add a blog to your website. Capable or not, Wordpress is not without its faults, one of which being that it needs a lot of memory and processor resources to function well. If you don't choose the right hosting, even a relatively small and simple WordPress site can run slowly (not good for visitors or from Google's perspective). The more visitors your site gets, the more resources and memory Wordpress uses. Shared website hosting comes with a series of restrictions on memory, CPU use and PHP usage/memory, which can make it unsuitable for Wordpress sites. Some hosting companies provide dedicated 'wordpress hosting' which is configured for better performance, but which is a little more expensive. In any event, as the number of visitors to your site increases, you will need to upgrade your hosting to allow for the increased memory and resource usage. It's true that there is more to it than is written above, but that's all you need to know to get started.