Every website is stored on a server that is owned and operated by a separate company
. Sometimes this is the company you purchase your domain name through but it isn't necessarily the case every time.
You're basically looking for someone to store the data for you, and allow access to your website. They often also offer ways to combat spam and have antivirus systems in place to protect your site. If they do not then it's probably not the best place for a business website to be parked.
In choosing a host one of the main things to consider beyond this is their downtime. All servers will go down at some point, generally for regular maintenance, if there is a power blackout where it is stored or for other reasons. You need to know what the chances are and what downtime statistics look like. Good hosts will have this information freely available on their website, including their back up power sources and percentage of time that websites will be live.
While 100% up time is ideal it may not be realistically possible but you're going to want a host that aims for it. If they can offer you 99%then this may be suitable, but remember that every time your website is unavailable people are turned away. They cannot access your contact details, any information at all in fact. It is as if your page doesn't exist and they will be told that their browser cannot locate it.
If this happens regularly the chances of losing business are high. It'll also lead to word of mouth that you are no longer in business, or at least stop people checking back - if you're turned away more than once without finding the business information at all then it'll be considered outdated and forgotten.