A lot of times people want hosting with access to root. But what does "root access" mean? Root, or getting root, is receiving the privledge to access all of the places on a computer. If you think of a server/computer as a tree the roots control the tree. The roots of a tree allow water in, minerals in and are the lifeblood of the tree. Anything which goes into the roots goes into the entire tree. Anything which affects the roots of a tree affects the entire tree.
Servers are set up with a similar thought process in that parts of the server are broken down into different areas. Each different area has its own privledges. One area cannot affect another area. For example, if there are three web sites on a server and one web site breaks the other two will not be affected. Each web site is in its own part of the server and can affect only itself. However, there has to be a master account or way into each area or site. If you don't have a master method to access all sites at once it would be a tremoundous amount of effort if something needed to be fixed or updated on every site on the server. The method or access to all of the parts of the server is "root access." When someone has root access they can affect everything on the entire server or change everything on the entire server. There are no restrictions with root access. If an error is made in root access it could "wipe out the entire server."
So why do people want root access? Who knows. But unless you are leasing your own server and need to affect every account on the server you don't need root access. There are some things you can do to make your site run more efficient with root access, but unless you know what you are doing you could destroy the entire server. And webhosting providers are not going to allow that to happen because chances are there is more than one client on the server. Besides that's what the webhosting company is being paid to do-manage the server where your hosting account is. It's not your job to manage the server, just to manage your own web site.