Hosting is a service provided (or fronted) by a company that maintains the computer servers that your website is loaded onto, making your website available on the internet.
Who offers this?
Not your web designer, it will be a third party company such as Go Daddy, Siteground, etc. However it is common for website owners to outsource the dealings with the hosting company to your web design agency, especially if your website agency will be managing the ongoing maintenance of your website.
Where are the best deals to be had?
It is a common practice for a Hosting Company to offer discounts to customers in Year One in order to win business and then hope the hassle of moving deters the client from refusing the full price increase in Year 2!
Server uptime is a key consideration when choosing a reliable service provider; 99.9% uptime is the minimum level you should accept, after all some providers offer 99% which may sound good until you realise this means your website can be offline for almost 4 whole days each year!
What should I expect to pay?
About £100 per year including VAT, though discounts may be available in your first year. This should get you one website hosted and give you a personalised email account based upon your domain name too.
Is there anything else I need to pay? You will also need your Domain name (i.e: OwnersWebsites.co.uk ). Go Daddy for example currently charge £12.99+VAT per year.
Is it easy to manage myself?
Yes, if your only direct interaction with the hosting company is limited to logging in to renew or cancel their service. Some technical understanding is recommended to troubleshoot issues or navigate around the service to upgrade or switch service to another provider. Some experience is recommended if you ever need to make sweeping changes to the back-end of your website.