The hosting might be inexpensive or free, but it is ineffective for search engines.
Some web hosting or domain name companies offer inexpensive (or free) hosting within a "frame". With this kind of installation it is possible to continue hosting the actual content on a free hosting provider (or anywhere at all) and to have it displayed when a user accesses the domain name. Often, the hosting company also displays advertising in a separate frame on the same page.
A setup like that is very bad with regards to wanting to get indexed in any search engine. The problem is that the actual content is not connected to the domain name -- it remains elsewhere. The only content available for the domain name is the "frameset" page, which often does not contain a lot of information (or none at all) about the actual site.
A frameset page could look like this:
The only indexable content on the domain is "Your browser does not support frames. (...) to enter the site". If a search engine were to index that page, it would only know that part -- everything else, the actual content and everything that belongs to the site, is not indexable under the domain name, it is on "myname.mysite.wanadoo-members.co.uk" and might be indexed with that domain name, if at all.<html><head><title></title></head>
<frameset rows='100%, *' frameborder=no framespacing=0 border=0>
<frame src="http://myname.mysite.wanadoo-members.co.uk" name=mainwindow frameborder=no
framespacing=0 marginheight=0 marginwidth=0></frame>
</frameset>
<noframes> <h2>Your browser does not support frames. We recommend upgrading your browser.</h2><br><br> <center>Click <a href="http://myname.mysite.wanadoo-members.co.uk">here</a> to enter the site.</center> </noframes></html>
Another problem with keeping the content on a different domain is that the content will attract the links and the link-value. This means that over time, the domain where the content is will gain value. In general this is not a problem, but free hosting often means that it can change, that you might need to move the content to another free hosting provider over time. If this happens when you are no longer able to access the old content, you can lose all value attachted to the content. By hosting the content on your own domain you will be able to keep the value for as long as you keep the domain name, regardless of which hosting provider you choose -- it will always be accessable through your domain name.
Additionally, a framed site is often bad for users as well - they will not be able to link directly to the content they are seeing. This could cause them to not link at all, which in turn could mean that your site can not gain value as it might otherwise. For the search engines, each link is a kind of recommendation for a site; with few links it is possible that the search engines do not regard the site as authoritive enough to merit a listing in the index (or a high ranking in the search results). A framed site will always have a disadvantage with regards to search engines.
Moving to normal hosting is usually fairly easy and straightforward. Once your hoster removes the frameset pages, you can usually just re-use your existing pages. The user will not notice much of a difference, but the search engines will start to find content. In addition, it makes sense to add a redirect from the old pages to the new ones - this is often done with a "meta-refresh redirect". The redirect is important: it will send the visitors and search engines to the new pages -- otherwise the old pages might remain indexed for a while, competing with your new content.
Once you have moved the content and set the site up in the way that you like, it always makes sense to promote it -- to tell other people about your new site. This is sometimes done with links, sometimes with traditional methods like newsletters, mailings, word of mouth, etc. The idea behind your promotion is that you want people to look at your site and to want to recommend it to others - you want them to link to your site. Good content will attract good links, but if nobody knows about your good content, it will not get any links.